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Artigos de revistas sobre o tema "Compact extensions"

Autor: Grafiati

Publicado: 14 de dezembro de 2024

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1

Gutik, Oleg, e Kateryna Pavlyk. "On pseudocompact topological Brandt λ0-extensions of semitopological monoids". Topological Algebra and its Applications 1 (31 de dezembro de 2013): 60–79. http://dx.doi.org/10.2478/taa-2013-0007.

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AbstractIn the paper we investigate topological properties of a topological Brandt λ0-extension B0λ(S) of a semitopological monoid S with zero. In particular we prove that for every Tychonoff pseudocompact (resp., Hausdorff countably compact, Hausdorff compact) semitopological monoid S with zero there exists a unique semiregular pseudocompact (resp., Hausdorff countably compact, Hausdorff compact) extension B0λ(S) of S and establish their Stone-Cˇ ech and Bohr compactifications. We also describe a category whose objects are ingredients in the constructions of pseudocompact (resp., countably compact, sequentially compact, compact) topological Brandt λ0- extensions of pseudocompact (resp., countably compact, sequentially compact, compact) semitopological monoids with zeros.

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2

Perán, Juan. "Locally compact multivector extensions". Journal of Mathematical Analysis and Applications 287, n.º 2 (novembro de 2003): 455–72. http://dx.doi.org/10.1016/s0022-247x(03)00542-0.

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KOUSHESH, M. R. "Topological extensions with compact remainder". Journal of the Mathematical Society of Japan 67, n.º 1 (janeiro de 2015): 1–42. http://dx.doi.org/10.2969/jmsj/06710001.

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4

KOUSHESH, M. R. "ONE-POINT CONNECTIFICATIONS". Journal of the Australian Mathematical Society 99, n.º 1 (9 de janeiro de 2015): 76–84. http://dx.doi.org/10.1017/s1446788714000676.

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A space $Y$ is called an extension of a space $X$ if $Y$ contains $X$ as a dense subspace. An extension $Y$ of $X$ is called a one-point extension if $Y\setminus X$ is a singleton. Compact extensions are called compactifications and connected extensions are called connectifications. It is well known that every locally compact noncompact space has a one-point compactification (known as the Alexandroff compactification) obtained by adding a point at infinity. A locally connected disconnected space, however, may fail to have a one-point connectification. It is indeed a long-standing question of Alexandroff to characterize spaces which have a one-point connectification. Here we prove that in the class of completely regular spaces, a locally connected space has a one-point connectification if and only if it contains no compact component.

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5

Berezovski, Tetyana, Oleg Gutik e Kateryna Pavlyk. "Brandt Extensions and Primitive Topological Inverse Semigroups". International Journal of Mathematics and Mathematical Sciences 2010 (2010): 1–13. http://dx.doi.org/10.1155/2010/671401.

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We study (countably) compact and (absolutely) -closed primitive topological inverse semigroups. We describe the structure of compact and countably compact primitive topological inverse semigroups and show that any countably compact primitive topological inverse semigroup embeds into a compact primitive topological inverse semigroup.

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6

Székelyhidi, László. "Harmonic Synthesis on Group Extensions". Mathematics 12, n.º 19 (27 de setembro de 2024): 3013. http://dx.doi.org/10.3390/math12193013.

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Harmonic synthesis describes translation invariant linear spaces of continuous complex valued functions on locally compact abelian groups. The basic result due to L. Schwartz states that such spaces on the reals are topologically generated by the exponential monomials in the space; in other words, the locally compact abelian group of the reals is synthesizable. This result does not hold for continuous functions in several real variables, as was shown by D.I. Gurevich’s counterexamples. On the other hand, if two discrete abelian groups have this synthesizability property, then so does their direct sum, as well. In this paper, we show that if two locally compact abelian groups have this synthesizability property and at least one of them is discrete, then their direct sum is synthesizable. In fact, more generally, we show that any extension of a synthesizable locally compact abelian group by a synthesizable discrete abelian group is synthesizable. This is an important step toward the complete characterization of synthesizable locally compact abelian groups.

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7

Sund, Terje. "Remarks on locally compact group extensions." MATHEMATICA SCANDINAVICA 69 (1 de dezembro de 1991): 199. http://dx.doi.org/10.7146/math.scand.a-12378.

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8

Kunen, Kenneth. "Compact scattered spaces in forcing extensions". Fundamenta Mathematicae 185, n.º 3 (2005): 261–66. http://dx.doi.org/10.4064/fm185-3-4.

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9

Nogura, Tsugunori. "Countably compact extensions of topological spaces". Topology and its Applications 23, n.º 3 (agosto de 1986): 313–14. http://dx.doi.org/10.1016/0166-8641(85)90049-5.

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10

Botelho, Geraldo, e Kuo Po Ling. "On compact extensions of multilinear operators". Bulletin of the Brazilian Mathematical Society, New Series 45, n.º 2 (junho de 2014): 343–53. http://dx.doi.org/10.1007/s00574-014-0052-z.

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11

Coelho, Zaqueu, e William Parry. "Shift endomorphisms and compact Lie extensions". Boletim da Sociedade Brasileira de Matem�tica 29, n.º 1 (março de 1998): 163–79. http://dx.doi.org/10.1007/bf01245872.

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12

Jakl, Tomáš. "Canonical extensions of locally compact frames". Topology and its Applications 273 (março de 2020): 106976. http://dx.doi.org/10.1016/j.topol.2019.106976.

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13

Narici, Lawrence, e Edward Beckenstein. "On Continuous Extensions". gmj 3, n.º 6 (dezembro de 1996): 565–70. http://dx.doi.org/10.1515/gmj.1996.565.

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Abstract We consider various possibilities concerning the continuous extension of continuous functions taking values in an ultrametric space. In Section 1 we consider Tietze-type extension theorems concerning continuous extendibility of continuous functions from compact and closed subsets to the whole space. In Sections 2 and 3 we consider extending “separated” continuous functions in such a way that certain continuous extensions remain separated. Functions taking values in a complete ultravalued field are dealt with in Section 2, and the real and complex cases in Section 3.

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14

Lipparini, Paolo. "Limit ultrapowers and abstract logics". Journal of Symbolic Logic 52, n.º 2 (junho de 1987): 437–54. http://dx.doi.org/10.2307/2274393.

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AbstractWe associate with any abstract logic L a family F(L) consisting, intuitively, of the limit ultrapowers which are complete extensions in the sense of L.For every countably generated [ω, ω]-compact logic L, our main applications are:(i) Elementary classes of L can be characterized in terms of ≡L only.(ii) If and are countable models of a countable superstable theory without the finite cover property, then .(iii) There exists the “largest” logic M such that complete extensions in the sense of M and L are the same; moreover M is still [ω, ω]-compact and satisfies an interpolation property stronger than unrelativized ⊿-closure.(iv) If L = Lωω(Qx), then cf(ωx) > ω and λω < ωx, for all λ < ωx.We also prove that no proper extension of Lωω generated by monadic quantifiers is compact. This strengthens a theorem of Makowsky and Shelah. We solve a problem of Makowsky concerning Lκλ-compact cardinals. We partially solve a problem of Makowsky and Shelah concerning the union of compact logics.

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15

Forrest, A. H. "Decomposing isometric extensions using group extensions". Ergodic Theory and Dynamical Systems 13, n.º 4 (dezembro de 1993): 661–73. http://dx.doi.org/10.1017/s0143385700007604.

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AbstractThis paper studies the structure of isometric extensions of compact metric topological dynamical systems with ℤ action and gives two decompositions of the general case to a more structured case. Suppose that Y → X is a M-isometric extension. An extension, Z, of Y is constructed which is also a G-isometric extension of X, where G is the group of isometries of M. The first construction shows that, provided that (X, T) is transitive, there are almost-automorphic extensions Y′ → Y and X′ → X, so that Y′ is homeomorphic to X′ × M and the natural projection Y′ → X′ is a group extension. The second shows that, provided that (X, T) is minimal, there is a G-action on Z which commutes with T and which preserves fibres and acts on each of them minimally. Each individual orbit closure, Za, in Z is a G′-isometric extension of X, where G′ is a subgroup of G, and there is a G′-action on Za which commutes with T, preserves fibres and acts minimally on each of them. Two illustrations are presented. Of the first: to reprove a result of Furstenberg; that every distal point is IP*-recurrent. Of the second: to describe the minimal subsets in isometric extensions of minimal topological dynamical systems.

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16

Chamashev, Marat, e Guliza Namazova. "ON COMPACTNESS TYPE EXTENSIONS OF TOPOLOGYCAL AND UNIFORM SPACES". Вестник Ошского государственного университета. Математика. Физика. Техника, n.º 1(4) (11 de junho de 2024): 247–50. http://dx.doi.org/10.52754/16948645_2024_1(4)_46.

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In this article extensions of real-complete Tychonoff and uniform spaces are considered, as well as locally compact paracompact and locally compact Lindelöff extensions of Tychonoff and uniform spaces.

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17

Brungs, Hans Heinrich, e Günter Törner. "Maximal immediate extensions are not necessarily maximally complete". Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 49, n.º 2 (outubro de 1990): 196–211. http://dx.doi.org/10.1017/s1446788700030482.

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AbstractAn extension R1 of a right chain ring R is called immediate if R1 has the same residue division ring and the same lattice of principal right ideals as R. Properties of such immediate extensions are studied. It is proved that for every R, maximal immediate extensions exist, but that in contrast to the commutative case maximal right chain rings are not necessarily linearly compact.

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18

Câmpeanu, Cezar. "Two Extensions of Cover Automata". Axioms 10, n.º 4 (10 de dezembro de 2021): 338. http://dx.doi.org/10.3390/axioms10040338.

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Deterministic Finite Cover Automata (DFCA) are compact representations of finite languages. Deterministic Finite Automata with “do not care” symbols and Multiple Entry Deterministic Finite Automata are both compact representations of regular languages. This paper studies the benefits of combining these representations to get even more compact representations of finite languages. DFCAs are extended by accepting either “do not care” symbols or considering multiple entry DFCAs. We study for each of the two models the existence of the minimization or simplification algorithms and their computational complexity, the state complexity of these representations compared with other representations of the same language, and the bounds for state complexity in case we perform a representation transformation. Minimization for both models proves to be NP-hard. A method is presented to transform minimization algorithms for deterministic automata into simplification algorithms applicable to these extended models. DFCAs with “do not care” symbols prove to have comparable state complexity as Nondeterministic Finite Cover Automata. Furthermore, for multiple entry DFCAs, we can have a tight estimate of the state complexity of the transformation into equivalent DFCA.

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19

Panchapagesan, T. V., e Shivappa Veerappa Palled. "On vector lattice-valued measures II". Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 40, n.º 2 (abril de 1986): 234–52. http://dx.doi.org/10.1017/s144678870002721x.

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AbstractFor a weakly (, )-distributive vector lattice V, it is proved that a V {}-valued Baire measure 0 on a locally compact Hausdorff space T admits uniquely regular Borel and weakly Borel extensions on T if and only if 0 is strongly regular at . Consequently, for such a vector lattice V every V-valued Baire measure on a locally compact Hausdorff space T has unique regular Borel and weakly Borel extensions. Finally some characterisations of a weakly (, )-distributive vector lattice are given in terms of the existence of regular Borel (weakly Borel) extensions of certain V {}-valued Barie measures on locally compact Hausdorff spaces.

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20

Porter, Jack, e Russell Woods. "When all semiregularH-closed extensions are compact". Pacific Journal of Mathematics 120, n.º 1 (1 de novembro de 1985): 179–88. http://dx.doi.org/10.2140/pjm.1985.120.179.

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21

Lopes, B. C., L. Ecco, E. C. Xavier e R. J. Azevedo. "Design and evaluation of compact ISA extensions". Microprocessors and Microsystems 40 (fevereiro de 2016): 1–15. http://dx.doi.org/10.1016/j.micpro.2015.09.010.

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22

Afrooz, Sosan, Abdolaziz Hesari e Alireza Salehi. "Realcompact and Lindelöf Extensions with Compact Remainder". Bulletin of the Iranian Mathematical Society 46, n.º 5 (10 de dezembro de 2019): 1223–42. http://dx.doi.org/10.1007/s41980-019-00322-3.

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23

Fiebig, Doris. "Common Extensions for Locally Compact Markov Shifts". Monatshefte f�r Mathematik 132, n.º 4 (1 de agosto de 2001): 289–301. http://dx.doi.org/10.1007/s006050170035.

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24

KOUSHESH, M. R. "ONE-POINT EXTENSIONS AND LOCAL TOPOLOGICAL PROPERTIES". Bulletin of the Australian Mathematical Society 88, n.º 1 (2 de agosto de 2012): 12–16. http://dx.doi.org/10.1017/s0004972712000524.

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AbstractA space $Y$ is called an extension of a space $X$ if $Y$ contains $X$ as a dense subspace. An extension $Y$ of $X$ is called a one-point extension of $X$ if $Y\setminus X$ is a singleton. P. Alexandroff proved that any locally compact non-compact Hausdorff space $X$ has a one-point compact Hausdorff extension, called the one-point compactification of $X$. Motivated by this, Mrówka and Tsai [‘On local topological properties. II’, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys.19 (1971), 1035–1040] posed the following more general question: For what pairs of topological properties ${\mathscr P}$ and ${\mathscr Q}$ does a locally-${\mathscr P}$ space $X$ having ${\mathscr Q}$ possess a one-point extension having both ${\mathscr P}$ and ${\mathscr Q}$? Here, we provide an answer to this old question.

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25

Thomsen, Klaus. "Ergodic actions of group extensions on von Neumann algebras". Proceedings of the Royal Society of Edinburgh: Section A Mathematics 112, n.º 1-2 (1989): 71–112. http://dx.doi.org/10.1017/s0308210500028183.

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SynopsisWe consider automorphic actions on von Neumann algebras of a locally compact group E given as a topological extension 0 → A → E → G → 0, where A is compact abelian and second countable. Motivated by the wish to describe and classify ergodic actions of E when G is finite, we classify (up to conjugacy) first the ergodic actions of locally compact groups on finite-dimensional factors and then compact abelian actions with the property that the fixed-point algebra is of type I with atomic centre. We then handle the case of ergodic actions of E with the property that the action is already ergodic when restricted to A, and then, as a generalisation, the case of (not necessarily ergodic) actions of E with the property that the restriction to A is an action with abelian atomic fixed-point algebra. Both these cases are handled for general locally compact-countable G. Finally, we combine the obtained results to classify the ergodic actions of E when G is finite, provided that either the extension is central and Hom (G, T) = 0, or G is abelian and either cyclic or of an order not divisible by a square.

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26

Glasner, Eli, e Bernard Host. "Extensions of Cantor minimal systems and dimension groups". crll 2013, n.º 682 (3 de maio de 2012): 207–43. http://dx.doi.org/10.1515/crelle-2012-0037.

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Abstract. Given a factor map of Cantor minimal systems, we study the relations between the dimension groups of the two systems. First, we interpret the torsion subgroup of the quotient of the dimension groups in terms of intermediate extensions which are extensions of (Y,S) by a compact abelian group. Then we show that, by contrast, the existence of an intermediate non-abelian finite group extension can produce a situation where the dimension group of (Y,S) embeds into a proper subgroup of the dimension group of (X,T), yet the quotient of the dimension groups is nonetheless torsion free. Next we define higher order cohomology groups associated to an extension, and study them in various cases (proximal extensions, extensions by, not necessarily abelian, finite groups, etc.). Our main result here is that all the cohomology groups are torsion groups. As a consequence we can now identify as the torsion group of the quotient group .

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27

GANSTER, MAXIMILIAN. "A NOTE ON SIMPLE EXTENSIONS AND SEMI-COMPACT TOPOLOGIES". Tamkang Journal of Mathematics 22, n.º 4 (1 de dezembro de 1991): 343–51. http://dx.doi.org/10.5556/j.tkjm.22.1991.4623.

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We study simple extensions of semi-compact topological spaces. Our main result says that if $X$ is an infinite set then maximal semi-compact topologies on $X$ do not exist.

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28

Krupiński, Krzysztof. "Generalizations of small profinite structures". Journal of Symbolic Logic 75, n.º 4 (dezembro de 2010): 1147–75. http://dx.doi.org/10.2178/jsl/1286198141.

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AbstractWe generalize the model theory of small profinite structures developed by Newelski to the case of compact metric spaces considered together with compact groups of homeomorphisms and satisfying the existence of m-independent extensions (we call them compact e-structures). We analyze the relationships between smallness and different versions of the assumption of the existence of m-independent extensions and we obtain some topological consequences of these assumptions. Using them, we adopt Newelski's proofs of various results about small profinite structures to compact e-structures. In particular, we notice that a variant of the group configuration theorem holds in this context.A general construction of compact structures is described. Using it, a class of examples of compact e-structures which are not small is constructed.It is also noticed that in an m-stable compact e-structure every orbit is equidominant with a product of m-regular orbits.

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29

Miao, Tianxuan. "The Extensions of an Invariant Mean and the Set LIM ∽ TLIM". Canadian Journal of Mathematics 46, n.º 4 (1 de agosto de 1994): 808–17. http://dx.doi.org/10.4153/cjm-1994-046-x.

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AbstractLet with . If G is a nondiscrete locally compact group which is amenable as a discrete group and m ∈ LIM(CB(G)), then we can embed into the set of all extensions of m to left invariant means on L∞(G) which are mutually singular to every element of TLIM(L∞(G)), where LIM(S) and TLIM(S) are the sets of left invariant means and topologically left invariant means on S with S = CB(G) or L∞(G). It follows that the cardinalities of LIM(L∞(G)) ̴ TLIM(L∞(G)) and LIM(L∞(G)) are equal. Note that which contains is a very big set. We also embed into the set of all left invariant means on CB(G) which are mutually singular to every element of TLIM(CB(G)) for G = G1 ⨯ G2, where G1 is nondiscrete, non–compact, σ–compact and amenable as a discrete group and G2 is any amenable locally compact group. The extension of any left invariant mean on UCB(G) to CB(G) is discussed. We also provide an answer to a problem raised by Rosenblatt.

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30

Reyes, Edgar N. "Homomorphisms of ergodic group actions and conjugacy of skew product actions". International Journal of Mathematics and Mathematical Sciences 19, n.º 4 (1996): 781–88. http://dx.doi.org/10.1155/s0161171296001081.

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LetGbe a locally compact group acting ergodically onX. We discuss relationships between homomorphisms on the measured groupoidX×G, conjugacy of skew product extensions, and similarity of measured groupoids. To do this, we describe the structure of homomorphisms onX×Gwhose restriction to an extension given by a skew product action is the trivial homomorphism.

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31

Inoue, Shin, e Anton E. Becker. "Posterior Extensions of the Human Compact Atrioventricular Node". Circulation 97, n.º 2 (20 de janeiro de 1998): 188–93. http://dx.doi.org/10.1161/01.cir.97.2.188.

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32

Robinson, E. Arthur. "Ergodic properties that lift to compact group extensions". Proceedings of the American Mathematical Society 102, n.º 1 (1 de janeiro de 1988): 61. http://dx.doi.org/10.1090/s0002-9939-1988-0915717-4.

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MELBOURNE, IAN, e MATTHEW NICOL. "STATISTICAL PROPERTIES OF ENDOMORPHISMS AND COMPACT GROUP EXTENSIONS". Journal of the London Mathematical Society 70, n.º 02 (outubro de 2004): 427–46. http://dx.doi.org/10.1112/s0024610704005587.

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Miley, George H. "Compact Tori as Extensions of the Spherical Tokamak". Fusion Technology 27, n.º 3T (abril de 1995): 382–86. http://dx.doi.org/10.13182/fst95-a11947111.

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Cho, Jin-Hwan, Min Kyu Kim e Dong Youp Suh. "On extensions of representations for compact Lie groups". Journal of Pure and Applied Algebra 178, n.º 3 (março de 2003): 245–54. http://dx.doi.org/10.1016/s0022-4049(02)00212-8.

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36

van Gool, Sam J. "Duality and canonical extensions for stably compact spaces". Topology and its Applications 159, n.º 1 (janeiro de 2012): 341–59. http://dx.doi.org/10.1016/j.topol.2011.09.040.

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Park, Sehie. "Extensions of best approximation and coincidence theorems". International Journal of Mathematics and Mathematical Sciences 20, n.º 4 (1997): 689–98. http://dx.doi.org/10.1155/s016117129700094x.

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LetXbe a Hausdorff compact space,Ea topological vector space on whichE*separates points,F:X→2Ean upper semicontinuous multifunction with compact acyclic values, andg:X→Ea continuous function such thatg(X)is convex andg−1(y)is acyclic for eachy∈g(X). Then either (1) there exists anx0∈Xsuch thatgx0∈Fx0or (2) there exist an(x0,z0)on the graph ofFand a continuous seminormponEsuch that0<p(gx0−z0)≤p(y−z0) for all y∈g(X). A generalization of this result and its application to coincidence theorems are obtained. Our aim in this paper is to unify and improve almost fifty known theorems of others.

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KOIKE, KAZUTOSHI. "MORITA DUALITY AND RING EXTENSIONS". Journal of Algebra and Its Applications 12, n.º 02 (16 de dezembro de 2012): 1250160. http://dx.doi.org/10.1142/s0219498812501605.

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In this paper, we show that there exists a category equivalence between certain categories of A-rings (respectively, ring extensions of A) and B-rings (respectively, ring extensions of B), where A and B are Morita dual rings. In this category equivalence, corresponding two A-ring and B-ring are Morita dual. This is an improvement of a result of Müller, which state that if a ring A has a Morita duality induced by a bimodule BQA and R is a ring extension of A such that RA and Hom A(R, Q)A are linearly compact, then R has a Morita duality induced by the bimodule S End R( Hom A(R, Q))R with S = End R( Hom A(R, Q)). We also investigate relationships between Morita duality and finite ring extensions. Particularly, we show that if A and B are Morita dual rings with B basic, then every finite triangular (respectively, normalizing) extension R of A is Morita dual to a finite triangular (respectively, normalizing) extension S of B, and we give a result about finite centralizing free extensions, which unify a result of Mano about self-duality and a result of Fuller–Haack about semigroup rings.

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Park, Efton. "Toeplitz Algebras and Extensions of Irrational Rotation Algebras". Canadian Mathematical Bulletin 48, n.º 4 (1 de dezembro de 2005): 607–13. http://dx.doi.org/10.4153/cmb-2005-056-2.

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AbstractFor a given irrational number θ, we define Toeplitz operators with symbols in the irrational rotation algebra , and we show that the C*-algebra generated by these Toeplitz operators is an extension of by the algebra of compact operators. We then use these extensions to explicitly exhibit generators of the group KK1(, ℂ). We also prove an index theorem for that generalizes the standard index theorem for Toeplitz operators on the circle.

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40

Sahleh, Hossein, e Ali Alijani. "Extensions of Locally Compact Abelian, Torsion-Free Groups by Compact Torsion Abelian Groups". British Journal of Mathematics & Computer Science 22, n.º 4 (10 de janeiro de 2017): 1–5. http://dx.doi.org/10.9734/bjmcs/2017/32966.

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BASEILHAC, P., P. GRANGÉ e M. RAUSCH DE TRAUBENBERG. "EXTENSION OF SINE–GORDON FIELD THEORY FROM GENERALIZED CLIFFORD ALGEBRAS". Modern Physics Letters A 13, n.º 31 (10 de outubro de 1998): 2531–39. http://dx.doi.org/10.1142/s0217732398002692.

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Linearization of homogeneous polynomials of degree n and k variables leads to generalized Clifford algebras. Multicomplex numbers are then introduced in analogy to complex numbers with respect to the usual Clifford algebra. In turn multi-complex extensions of trigonometric functions are constructed in terms of "compact" and "non-compact" variables. It gives rise to the natural extension of the d-dimensional sine–Gordon field theory in the n-dimensional multicomplex space. In two dimensions, the cases n = 1, 2, 3, 4 are identified as the quantum integrable Liouville, sine–Gordon and known deformed Toda models. The general case is discussed.

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Malamud, M. M. "TO THE BIRMAN–KREIN–VISHIK THEORY". Доклады Российской академии наук. Математика, информатика, процессы управления 509, n.º 1 (1 de janeiro de 2023): 54–59. http://dx.doi.org/10.31857/s2686954322600574.

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Let A ≥ mA 0 be a closed positive definite symmetric operator in a Hilbert space ℌ, let \({{\hat {A}}_{F}}\) and \({{\hat {A}}_{K}}\) be its Friedrichs and Krein extensions, and let ∞ be the ideal of compact operators in ℌ. The following problem has been posed by M.S. Birman: Is the implication A–1 ∈ G∞ ⇒ (\({{\hat {A}}_{F}}\) )–1 ∈ G∞(ℌ) holds true or not? It turns out that under condition A–1 ∈ G∞ the spectrum of Friedrichs extension \({{\hat {A}}_{F}}\) might be of arbitrary nature. This gives a complete negative solution to the Birman problem.Let \(\hat {A}_{K}^{'}\) be the reduced Krein extension. It is shown that certain spectral properties of the operators (\({{I}_{{{{\mathfrak{M}}_{0}}}}}\) + \(\hat {A}_{K}^{'}\))–1 and P1(I + A)–1 are close. For instance, these operators belong to a symmetrically normed ideal G, say are compact, only simultaneously. Moreover, it turns out that under a certain additional condition the eigenvalues of these operators have the same asymptotic.Besides we complete certain investigations by Birman and Grubb regarding the equivalence of semiboubdedness property of selfadjoint extensions of A and the corresponding boundary operators.

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Ionescu, Marius, Alex Kumjian, Aidan Sims e Dana P. Williams. "The Dixmier-Douady classes of certain groupoid C∗-algebras with continuous trace". Journal of Operator Theory 81, n.º 2 (15 de março de 2019): 407–31. http://dx.doi.org/10.7900/jot.2018mar07.2209.

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Given a locally compact abelian group G, we give an explicit formula for the Dixmier-Douady invariant of the C∗-algebra of the groupoid extension associated to a Cech 2-cocycle in the sheaf of germs of continuous G-valued functions. We then exploit the blow-up construction for groupoids to extend this to some more general central extensions of etale equivalence relations.

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BABICHEV, ANDREY, ROBERT M. BURTON e ADAM FIELDSTEEL. "Speedups of ergodic group extensions". Ergodic Theory and Dynamical Systems 33, n.º 4 (1 de maio de 2012): 969–82. http://dx.doi.org/10.1017/s0143385712000107.

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AbstractWe prove that for all ergodic extensions $S_{1}$ of a transformation by a locally compact second countable group $G$, and for all $G$-extensions $ S_{2} $ of an aperiodic transformation, there is a relative speedup of $ S_{1} $ that is relatively isomorphic to $S_{2}$. We apply this result to give necessary and sufficient conditions for two ergodic $n$-point or countable extensions to be related in this way.

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45

Villaveces, Andrés. "Heights of models of ZFC and the existence of end elementary extensions II". Journal of Symbolic Logic 64, n.º 3 (setembro de 1999): 1111–24. http://dx.doi.org/10.2307/2586621.

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AbstractThe existence of End Elementary Extensions of modelsM of ZFC is related to the ordinal height of M, according to classical results due to Keisler, Morley and Silver. In this paper, we further investigate the connection between the height of M and the existence of End Elementary Extensions of M. In particular, we prove that the theory ‘ZFC + GCH + there exist measurable cardinals + all inaccessible non weakly compact cardinals are possible heights of models with no End Elementary Extensions’ is consistent relative to the theory ‘ZFC + GCH + there exist measurable cardinals + the weakly compact cardinals are cofinal in ON’. We also provide a simpler coding that destroys GCH but otherwise yields the same result.

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Alijani, Aliakbar. "The 2-fold pure extensions need not split". New Zealand Journal of Mathematics 54 (25 de junho de 2023): 13–15. http://dx.doi.org/10.53733/277.

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Fendler, Gero, e Michael Leinert. "Convolution dominated operators on compact extensions of abelian groups". Advances in Operator Theory 4, n.º 1 (janeiro de 2019): 99–112. http://dx.doi.org/10.15352/aot.1712-1275.

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Dolgopyat, D. "Livsiĉ Theory for Compact Group Extensions of Hyperbolic Systems". Moscow Mathematical Journal 5, n.º 1 (2005): 55–66. http://dx.doi.org/10.17323/1609-4514-2005-5-1-55-66.

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Field, Michael, e William Parry. "STABLE ERGODICITY OF SKEW EXTENSIONS BY COMPACT LIE GROUPS". Topology 38, n.º 1 (janeiro de 1999): 167–87. http://dx.doi.org/10.1016/s0040-9383(98)00008-1.

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Ahn, Young-Ho. "A class of compact group extensions of Gauss transformation". Indagationes Mathematicae 13, n.º 3 (2002): 281–86. http://dx.doi.org/10.1016/s0019-3577(02)80011-8.

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