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Journal articles on the topic 'Compactly generated'

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Published: 11 March 2023

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1

Ross, Kenneth A. "Closed subgroups of compactly generated LCA groups are compactly generated." Topology and its Applications 259 (June 2019): 378–83. http://dx.doi.org/10.1016/j.topol.2019.02.042.

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2

Fujita, Hiroshi, and Dimitri Shakhmatov. "Topological groups with dense compactly generated subgroups." Applied General Topology 3, no. 1 (April 1, 2002): 85. http://dx.doi.org/10.4995/agt.2002.2115.

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<p>A topological group G is: (i) compactly generated if it contains a compact subset algebraically generating G, (ii) -compact if G is a union of countably many compact subsets, (iii) <sub>0</sub>-bounded if arbitrary neighborhood U of the identity element of G has countably many translates xU that cover G, and (iv) finitely generated modulo open sets if for every non-empty open subset U of G there exists a finite set F such that F U algebraically generates G. We prove that: (1) a topological group containing a dense compactly generated subgroup is both <sub>0</sub>-bounded and finitely generated modulo open sets, (2) an almost metrizable topological group has a dense compactly generated subgroup if and only if it is both <sub>0</sub>-bounded and finitely generated modulo open sets, and (3) an almost metrizable topological group is compactly generated if and only if it is -compact and finitely generated modulo open sets.</p>
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3

BATTENFELD, INGO, MATTHIAS SCHRÖDER, and ALEX SIMPSON. "Compactly generated domain theory." Mathematical Structures in Computer Science 16, no. 02 (April 2006): 141. http://dx.doi.org/10.1017/s0960129506005202.

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4

Neeman, Amnon. "Non-compactly generated categories." Topology 37, no. 5 (March 1998): 981–87. http://dx.doi.org/10.1016/s0040-9383(97)00069-4.

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5

Pestov, V. G. "Compactly generated topological groups." Mathematical Notes of the Academy of Sciences of the USSR 40, no. 5 (November 1986): 880–82. http://dx.doi.org/10.1007/bf01159710.

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6

James, Ioan M. "Fibrewise compactly-generated spaces." Publications of the Research Institute for Mathematical Sciences 31, no. 1 (1995): 45–61. http://dx.doi.org/10.2977/prims/1195164790.

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7

Holm, Henrik, and Peter Jørgensen. "Compactly generated homotopy categories." Homology, Homotopy and Applications 9, no. 1 (2007): 257–74. http://dx.doi.org/10.4310/hha.2007.v9.n1.a11.

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8

Escardó, Martín H. "Compactly generated Hausdorff locales." Annals of Pure and Applied Logic 137, no. 1-3 (January 2006): 147–63. http://dx.doi.org/10.1016/j.apal.2005.05.020.

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9

Bagley, R. W., T. S. Wu, and J. S. Yang. "Compact and compactly generated subgroups of locally compact groups." Proceedings of the American Mathematical Society 108, no. 4 (April 1, 1990): 1085. http://dx.doi.org/10.1090/s0002-9939-1990-0993738-2.

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10

Salmi, Pekka. "Quasi-actions and generalised Cayley–Abels graphs of locally compact groups." Journal of Group Theory 18, no. 1 (January 1, 2015): 45–60. http://dx.doi.org/10.1515/jgth-2014-0031.

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Abstract We define the notion of generalised Cayley–Abels graph for compactly generated locally compact groups in terms of quasi-actions. This extends the notion of Cayley–Abels graph of a compactly generated totally disconnected locally compact group, studied in particular by Krön and Möller under the name of rough Cayley graph (and relative Cayley graph). We construct a generalised Cayley–Abels graph for any compactly generated locally compact group using quasi-lattices and show uniqueness up to quasi-isometry. A class of examples is given by the Cayley graphs of cocompact lattices in compactly generated groups. As an application, we show that a compactly generated group has polynomial growth if and only if its generalised Cayley–Abels graph has polynomial growth (same for intermediate and exponential growth). Moreover, a unimodular compactly generated group is amenable if and only if its generalised Cayley–Abels graph is amenable as a metric space.
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11

Niederle, Josef. "On completely meet-irreducible elements in compactly generated lattices." Czechoslovak Mathematical Journal 39, no. 3 (1989): 490–91. http://dx.doi.org/10.21136/cmj.1989.102321.

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12

Piskunov, A. G. "Weight of compactly generated groups." Mathematical Notes of the Academy of Sciences of the USSR 49, no. 4 (April 1991): 406–8. http://dx.doi.org/10.1007/bf01158219.

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13

Grime, Matthew, and Peter Jørgensen. "Compactly Generated Relative Stable Categories." Algebras and Representation Theory 14, no. 2 (December 10, 2009): 247–51. http://dx.doi.org/10.1007/s10468-009-9187-9.

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14

LOSERT, V. "ON THE STRUCTURE OF GROUPS WITH POLYNOMIAL GROWTH II." Journal of the London Mathematical Society 63, no. 3 (June 2001): 640–54. http://dx.doi.org/10.1017/s0024610701001983.

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15

Chen, Wenjing, Zhongkui Liu, and Xiaoyan Yang. "Compactly generated triangulated subcategories of homotopy categories induced by cotorsion pairs." Journal of Algebra and Its Applications 17, no. 09 (August 23, 2018): 1850180. http://dx.doi.org/10.1142/s0219498818501803.

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In this paper, we investigate the homotopy categories [Formula: see text] and [Formula: see text] with respect to a complete and hereditary cotorsion pair [Formula: see text] in a bicomplete abelian category. We prove that [Formula: see text] is compactly generated provided that [Formula: see text] is compactly generated. We introduce and characterize Gorenstein [Formula: see text]-complexes with respect to [Formula: see text] and show that a complex is a Gorenstein [Formula: see text]-complex if and only if its every term is a Gorenstein [Formula: see text]-object. We also show that the inclusion functors [Formula: see text] and [Formula: see text] have right adjoints respectively when [Formula: see text] is compactly generated.
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16

Caprace, Pierre-Emmanuel, and Yves Cornulier. "On embeddings into compactly generated groups." Pacific Journal of Mathematics 269, no. 2 (July 26, 2014): 305–21. http://dx.doi.org/10.2140/pjm.2014.269.305.

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17

Willis, G. "Totally disconnected, nilpotent, locally compact groups." Bulletin of the Australian Mathematical Society 55, no. 1 (February 1997): 143–46. http://dx.doi.org/10.1017/s0004972700030604.

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It is shown that, if G is a totally disconnected, compactly generated and nilpotent locally compact group, then it has a base of neighbourhoods of the identity consisting of compact, open, normal subgroups. An example is given showing that the hypothesis that G be compactly generated is necessary.
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18

Bagley, R. W., T. S. Wu, and J. S. Yang. "Compactly generated subgroups and open subgroups of locally compact groups." Proceedings of the American Mathematical Society 103, no. 3 (March 1, 1988): 969. http://dx.doi.org/10.1090/s0002-9939-1988-0947692-0.

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19

CAPRACE, PIERRE-EMMANUEL, and NICOLAS MONOD. "Decomposing locally compact groups into simple pieces." Mathematical Proceedings of the Cambridge Philosophical Society 150, no. 1 (September 2, 2010): 97–128. http://dx.doi.org/10.1017/s0305004110000368.

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AbstractWe present a contribution to the structure theory of locally compact groups. The emphasis is on compactly generated locally compact groups which admit no infinite discrete quotient. It is shown that such a group possesses a characteristic cocompact subgroup which is either connected or admits a non-compact non-discrete topologically simple quotient. We also provide a description of characteristically simple groups and of groups all of whose proper quotients are compact. We show that Noetherian locally compact groups without infinite discrete quotient admit a subnormal series with all subquotients compact, compactly generated Abelian, or compactly generated topologically simple.Two appendices introduce results and examples around the concept of quasi-product.
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20

Fujita, Hiroshi, and Dmitri Shakhmatov. "A characterization of compactly generated metric groups." Proceedings of the American Mathematical Society 131, no. 3 (July 17, 2002): 953–61. http://dx.doi.org/10.1090/s0002-9939-02-06736-9.

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21

Oncina, L. "On Weakly-Compactly Generated Asplund Banach spaces." Quarterly Journal of Mathematics 55, no. 1 (March 1, 2004): 77–85. http://dx.doi.org/10.1093/qmath/hag036.

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22

Reid, Colin D., and Phillip R. Wesolek. "The essentially chief series of a compactly generated locally compact group." Mathematische Annalen 370, no. 1-2 (September 21, 2017): 841–61. http://dx.doi.org/10.1007/s00208-017-1597-0.

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23

Reid, Colin D. "Distal actions on coset spaces in totally disconnected locally compact groups." Journal of Topology and Analysis 12, no. 02 (September 28, 2018): 491–532. http://dx.doi.org/10.1142/s1793525319500523.

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Let [Formula: see text] be a totally disconnected locally compact (t.d.l.c.) group and let [Formula: see text] be an equicontinuously (for example, compactly) generated group of automorphisms of [Formula: see text]. We show that every distal action of [Formula: see text] on a coset space of [Formula: see text] is a SIN action, with the small invariant neighborhoods arising from open [Formula: see text]-invariant subgroups. We obtain a number of consequences for the structure of the collection of open subgroups of a t.d.l.c. group. For example, it follows that for every compactly generated subgroup [Formula: see text] of [Formula: see text], there is a compactly generated open subgroup [Formula: see text] of [Formula: see text] such that [Formula: see text] and such that every open subgroup of [Formula: see text] containing a finite index subgroup of [Formula: see text] contains a finite index subgroup of [Formula: see text]. We also show that for a large class of closed subgroups [Formula: see text] of [Formula: see text] (including for instance all closed subgroups [Formula: see text] such that [Formula: see text] is an intersection of subnormal subgroups of open subgroups), every compactly generated open subgroup of [Formula: see text] can be realized as [Formula: see text] for an open subgroup of [Formula: see text].
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24

Lajara, Sebastián, and José Rodríguez. "Strongly Asplund generated and strongly conditionally weakly compactly generated Banach spaces." Monatshefte für Mathematik 181, no. 1 (August 7, 2015): 103–16. http://dx.doi.org/10.1007/s00605-015-0804-x.

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25

BEROS, KONSTANTINOS A. "UNIVERSAL SUBGROUPS OF POLISH GROUPS." Journal of Symbolic Logic 79, no. 4 (December 2014): 1148–83. http://dx.doi.org/10.1017/jsl.2013.40.

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AbstractGiven a class${\cal C}$of subgroups of a topological groupG, we say that a subgroup$H \in {\cal C}$is auniversal${\cal C}$subgroupofGif every subgroup$K \in {\cal C}$is a continuous homomorphic preimage ofH. Such subgroups may be regarded as complete members of${\cal C}$with respect to a natural preorder on the set of subgroups ofG. We show that for any locally compact Polish groupG, the countable powerGωhas a universalKσsubgroup and a universal compactly generated subgroup. We prove a weaker version of this in the nonlocally compact case and provide an example showing that this result cannot readily be improved. Additionally, we show that many standard Banach spaces (viewed as additive topological groups) have universalKσand compactly generated subgroups. As an aside, we explore the relationship between the classes ofKσand compactly generated subgroups and give conditions under which the two coincide.
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26

Möller, Rögnvaldur G. "$FC^-$-elements in totally disconnected groups and automorphisms of infinite graphs." MATHEMATICA SCANDINAVICA 92, no. 2 (June 1, 2003): 261. http://dx.doi.org/10.7146/math.scand.a-14404.

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An element in a topological group is called an $\mathrm{FC}^-$-element if its conjugacy class has compact closure. The $\mathrm{FC}^-$-elements form a normal subgroup. In this note it is shown that in a compactly generated totally disconnected locally compact group this normal subgroup is closed. This result answers a question of Ghahramani, Runde and Willis. The proof uses a result of Trofimov about automorphism groups of graphs and a graph theoretical interpretation of the condition that the group is compactly generated.
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27

MEIGNIEZ, Gaël. "A compactly generated pseudogroup which is not realizable." Journal of the Mathematical Society of Japan 62, no. 4 (October 2010): 1205–18. http://dx.doi.org/10.2969/jmsj/06241205.

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28

MEIGNIEZ, Gaël. "Realizing compactly generated pseudo-groups of dimension one." Journal of the Mathematical Society of Japan 68, no. 4 (October 2016): 1747–75. http://dx.doi.org/10.2969/jmsj/06841747.

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29

Motamedi, M. "Compactly generated lattices with a unique essential element." International Journal of Algebra 1 (2007): 321–26. http://dx.doi.org/10.12988/ija.2007.07035.

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30

Pauksztello, David. "A Note on Compactly Generated Co-t-Structures." Communications in Algebra 40, no. 2 (February 2012): 386–94. http://dx.doi.org/10.1080/00927872.2010.528714.

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31

Ribeiro, Willian. "Compactly Generated Spaces and Quasi-spaces in Topology." Applied Categorical Structures 28, no. 4 (January 18, 2020): 539–73. http://dx.doi.org/10.1007/s10485-019-09589-3.

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32

Avilés, A., G. Plebanek, and J. Rodríguez. "The McShane integral in weakly compactly generated spaces." Journal of Functional Analysis 259, no. 11 (December 2010): 2776–92. http://dx.doi.org/10.1016/j.jfa.2010.08.007.

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33

Kolodyazhny, V. M. "Compactly supported functions generated by a polyharmonic operator." Cybernetics and Systems Analysis 42, no. 5 (September 2006): 730–42. http://dx.doi.org/10.1007/s10559-006-0112-5.

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34

Erné, Marcel. "Compact generation in partially ordered sets." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 42, no. 1 (February 1987): 69–83. http://dx.doi.org/10.1017/s1446788700033966.

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AbstractSeveral “classical” results on algebraic complete lattices extend to algebraic posets and, more generally, to so called compactly generated posets; but, of course, there may arise difficulties in the absence of certain joins or meets. For example, the property of weak atomicity turns out to be valid in all Dedekind complete compactly generated posets, but not in arbitrary algebraic posets. The compactly generated posets are, up to isomorphism, the inductive centralized systems, where a system of sets is called centralized if it contains all point closures. A similar representation theorem holds for algebraic posets; it is known that every algebraic poset is isomorphic to the system i(Q) of all directed lower sets in some poset Q; we show that only those posets P which satisfy the ascending chain condition are isomorphic to their own “up-completion” i(P). We also touch upon a few structural aspects such as the formation of direct sums, products and substructures. The note concludes with several applications of a generalized version of the Birkhoff Frink decomposition theorem for algebraic lattices.
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35

Nieto, Eduardo. "ON $M$-STRUCTURE AND WEAKLY COMPACTLY GENERATED BANACH SPACES." Proceedings of the Edinburgh Mathematical Society 46, no. 3 (October 2003): 679–86. http://dx.doi.org/10.1017/s0013091501000839.

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AbstractIt is well known that every non-reflexive $M$-ideal is weakly compactly generated (in short, WCG). We present a family of Banach spaces $\{V_{s}:0 \lt s \lt 1\}$ which are not WCG and such that every $V_{s}$ satisfies the inequality$$ \|\f\|\geq\|\pi\f\|+s\|\f-\pi\f\|\quad\forall\f\in V_{s}^{\ast\ast\ast}, $$where $\pi$ is the canonical projection from $V_{s}^{\ast\ast\ast}$ onto $V_{s}^{\ast}$. In particular, no $V_{s}$ can be renormed to be an $M$-ideal.AMS 2000 Mathematics subject classification: Primary 46B20
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36

Shin’ya, Hitoshi. "Spherical matrix functions and Banach representability for compactly generated locally compact motion groups." Journal of Mathematics of Kyoto University 38, no. 1 (1998): 167–200. http://dx.doi.org/10.1215/kjm/1250518165.

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37

Alghamdi, Azza, Maciej Klimek, and Marta Kosek. "Attractors of Compactly Generated Semigroups of Regular Polynomial Mappings." Complexity 2018 (November 11, 2018): 1–11. http://dx.doi.org/10.1155/2018/5698021.

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We investigate the metric space of pluriregular sets as well as the contractions on that space induced by infinite compact families of proper polynomial mappings of several complex variables. The topological semigroups generated by such families, with composition as the semigroup operation, lead to the constructions of a variety of Julia-type pluriregular sets. The generating families can also be viewed as infinite iterated function systems with compact attractors. We show that such attractors can be approximated both deterministically and probabilistically in a manner of the classic chaos game.
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38

Escardó, Martín, Jimmie Lawson, and Alex Simpson. "Comparing Cartesian closed categories of (core) compactly generated spaces." Topology and its Applications 143, no. 1-3 (August 2004): 105–45. http://dx.doi.org/10.1016/j.topol.2004.02.011.

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39

Sobecki, Dave. "A Characterization of Strongly Weakly Compactly Generated Banach Spaces." Rocky Mountain Journal of Mathematics 34, no. 4 (December 2004): 1503–5. http://dx.doi.org/10.1216/rmjm/1181069812.

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40

Fabian, M., and J. H. M. Whitfield. "On Equivalent Characterizations of Weakly Compactly Generated Banach Spaces." Rocky Mountain Journal of Mathematics 24, no. 4 (December 1994): 1363–78. http://dx.doi.org/10.1216/rmjm/1181072343.

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41

Gao, Nan, and Chrysostomos Psaroudakis. "Ladders of Compactly Generated Triangulated Categories and Preprojective Algebras." Applied Categorical Structures 26, no. 4 (November 21, 2017): 657–79. http://dx.doi.org/10.1007/s10485-017-9508-9.

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42

KORTCHEMSKI, IGOR, and CYRIL MARZOUK. "Simply Generated Non-Crossing Partitions." Combinatorics, Probability and Computing 26, no. 4 (March 28, 2017): 560–92. http://dx.doi.org/10.1017/s0963548317000050.

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We introduce and study the model of simply generated non-crossing partitions, which are, roughly speaking, chosen at random according to a sequence of weights. This framework encompasses the particular case of uniform non-crossing partitions with constraints on their block sizes. Our main tool is a bijection between non-crossing partitions and plane trees, which maps such simply generated non-crossing partitions into simply generated trees so that blocks of sizekare in correspondence with vertices of out-degreek. This allows us to obtain limit theorems concerning the block structure of simply generated non-crossing partitions. We apply our results in free probability by giving a simple formula relating the maximum of the support of a compactly supported probability measure on the real line in terms of its free cumulants.
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43

Christiansen, Lasse Hjuler, and Ole Christensen. "CONSTRUCTION OF SMOOTH COMPACTLY SUPPORTED WINDOWS GENERATING DUAL PAIRS OF GABOR FRAMES." Asian-European Journal of Mathematics 06, no. 01 (March 2013): 1350011. http://dx.doi.org/10.1142/s1793557113500113.

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Let g be any real-valued, bounded and compactly supported function, whose integer-translates {Tkg}k∈ℤ form a partition of unity. Based on a new construction of dual windows associated with Gabor frames generated by g, we present a method to explicitly construct dual pairs of Gabor frames. This new method of construction is based on a family of polynomials which is closely related to the Daubechies polynomials, used in the construction of compactly supported wavelets. For any k ∈ ℕ ∪ {∞} we consider the Meyer scaling functions and use these to construct compactly supported windows g ∈ Ck(ℝ) associated with a family of smooth compactly supported dual windows [Formula: see text]. For any n ∈ ℕ the pair of dual windows g, hn ∈ Ck(ℝ) have compact support in the interval [-2/3, 2/3] and share the property of being constant on half the length of their support. We therefore obtain arbitrary smoothness of the dual pair of windows g, hn without increasing their support.
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44

Angeleri Hügel, Lidia, and Michal Hrbek. "Parametrizing torsion pairs in derived categories." Representation Theory of the American Mathematical Society 25, no. 23 (July 30, 2021): 679–731. http://dx.doi.org/10.1090/ert/579.

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We investigate parametrizations of compactly generated t-structures, or more generally, t-structures with a definable coaisle, in the unbounded derived category D ( M o d - A ) \mathrm {D}({\mathrm {Mod}}\text {-}A) of a ring A A . To this end, we provide a construction of t-structures from chains in the lattice of ring epimorphisms starting in A A , which is a natural extension of the construction of compactly generated t-structures from chains of subsets of the Zariski spectrum known for the commutative noetherian case. We also provide constructions of silting and cosilting objects in D ( M o d - A ) \mathrm {D}({\mathrm {Mod}}\text {-}A) . This leads us to classification results over some classes of commutative rings and over finite dimensional hereditary algebras.
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45

Guan, Ai, and Andrey Lazarev. "Koszul duality for compactly generated derived categories of second kind." Journal of Noncommutative Geometry 15, no. 4 (December 7, 2021): 1355–71. http://dx.doi.org/10.4171/jncg/438.

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46

Garncarek, Ł. "Property of rapid decay for extensions of compactly generated groups." Publicacions Matemàtiques 59 (July 1, 2015): 301–12. http://dx.doi.org/10.5565/publmat_59215_02.

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47

FABIAN, M., V. MONTESINOS, and V. ZIZLER. "A CHARACTERIZATION OF SUBSPACES OF WEAKLY COMPACTLY GENERATED BANACH SPACES." Journal of the London Mathematical Society 69, no. 02 (March 29, 2004): 457–64. http://dx.doi.org/10.1112/s0024610703005118.

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48

Paseka, Jan, and Zdenka Riečanová. "Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras." International Journal of Theoretical Physics 49, no. 12 (April 15, 2009): 3216–23. http://dx.doi.org/10.1007/s10773-009-0011-4.

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49

Carchedi, David. "Compactly generated stacks: A Cartesian closed theory of topological stacks." Advances in Mathematics 229, no. 6 (April 2012): 3339–97. http://dx.doi.org/10.1016/j.aim.2012.02.006.

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50

Gao, Nan, and Xiaojing Xu. "Homological epimorphisms, compactly generated t-structures and Gorenstein-projective modules." Chinese Annals of Mathematics, Series B 39, no. 1 (January 2018): 47–58. http://dx.doi.org/10.1007/s11401-018-1050-z.

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