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Journal articles on the topic 'Compact Hausdorff spaces'

Author: Grafiati

Published: 4 June 2021

Last updated: 3 February 2022

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1

Bezhanishvili, G., N. Bezhanishvili, and J. Harding. "Modal compact Hausdorff spaces." Journal of Logic and Computation 25, no. 1 (2012): 1–35. http://dx.doi.org/10.1093/logcom/exs030.

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2

Garg, G. L., and Asha Goel. "Perfect maps in compact (countably compact) spaces." International Journal of Mathematics and Mathematical Sciences 18, no. 4 (1995): 773–76. http://dx.doi.org/10.1155/s0161171295000998.

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3

Nayar, Bhamini M. P. "Compact and extremally disconnected spaces." International Journal of Mathematics and Mathematical Sciences 2004, no. 20 (2004): 1047–56. http://dx.doi.org/10.1155/s0161171204208249.

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Viglino defined a Hausdorff topological space to beC-compact if each closed subset of the space is anH-set in the sense of Veličko. In this paper, we study the class of Hausdorff spaces characterized by the property that each closed subset is anS-set in the sense of Dickman and Krystock. Such spaces are calledC-s-compact. Recently, the notion of strongly subclosed relation, introduced by Joseph, has been utilized to characterizeC-compact spaces as those with the property that each function from the space to a Hausdorff space with a strongly subclosed inverse is closed. Here, it is shown thatC-

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4

Gruenhage, Gary. "Partitions of compact Hausdorff spaces." Fundamenta Mathematicae 142, no. 1 (1993): 89–100. http://dx.doi.org/10.4064/fm-142-1-89-100.

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5

Belugin, V. I., A. V. Osipov, and E. G. Pytkeev. "Compact condensations of Hausdorff spaces." Acta Mathematica Hungarica 164, no. 1 (2021): 15–27. http://dx.doi.org/10.1007/s10474-021-01131-z.

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6

XU, YATAO, and TANJA GRUBBA. "On computably locally compact Hausdorff spaces." Mathematical Structures in Computer Science 19, no. 1 (2009): 101–17. http://dx.doi.org/10.1017/s0960129508007366.

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Locally compact Hausdorff spaces generalise Euclidean spaces and metric spaces from ‘metric’ to ‘topology’. But does the effectivity on the latter (Brattka and Weihrauch 1999; Weihrauch 2000) still hold for the former? In fact, some results will be totally changed. This paper provides a complete investigation of a specific kind of space – computably locally compact Hausdorff spaces. First we characterise this type of effective space, and then study computability on closed and compact subsets of them. We use the framework of the representation approach, TTE, where continuity and computability o

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7

Bankston, Paul. "Reduced coproducts of compact Hausdorff spaces." Journal of Symbolic Logic 52, no. 2 (1987): 404–24. http://dx.doi.org/10.2307/2274391.

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AbstractBy analyzing how one obtains the Stone space of the reduced product of an indexed collection of Boolean algebras from the Stone spaces of those algebras, we derive a topological construction, the “reduced coproduct”, which makes sense for indexed collections of arbitrary Tichonov spaces. When the filter in question is an ultrafilter, we show how the “ultracoproduct” can be obtained from the usual topological ultraproduct via a compactification process in the style of Wallman and Frink. We prove theorems dealing with the topological structure of reduced coproducts (especially ultracopro

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8

Gurevic, R. "On Ultracoproducts of Compact Hausdorff Spaces." Journal of Symbolic Logic 53, no. 1 (1988): 294. http://dx.doi.org/10.2307/2274446.

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9

Gurevič, R. "On ultracoproducts of compact hausdorff spaces." Journal of Symbolic Logic 53, no. 1 (1988): 294–300. http://dx.doi.org/10.1017/s002248120002911x.

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AbstractI present solutions to several questions of Paul Bankston [2] by means of another version of the ultracoproduct construction, and explain the relation of ultracoproduct of compact Hausdorff spaces to other constructions combining topology, algebra and logic.

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10

Lee, Kyung Bok, and Song Yi Kim. "CHAIN RECURRENCES ON COMPACT HAUSDORFF SPACES." Far East Journal of Mathematical Sciences (FJMS) 101, no. 11 (2017): 2533–63. http://dx.doi.org/10.17654/ms101112533.

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11

Günther, Bernd. "Strong shape of compact Hausdorff spaces." Topology and its Applications 42, no. 2 (1991): 165–74. http://dx.doi.org/10.1016/0166-8641(91)90024-g.

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12

Bezhanishvili, G., D. Gabelaia, J. Harding, and M. Jibladze. "Compact Hausdorff Spaces with Relations and Gleason Spaces." Applied Categorical Structures 27, no. 6 (2019): 663–86. http://dx.doi.org/10.1007/s10485-019-09573-x.

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13

Mirotin, Adolf R. "Hausdorff operators on homogeneous spaces of locally compact groups." Journal of the Belarusian State University. Mathematics and Informatics, no. 2 (July 30, 2020): 28–35. http://dx.doi.org/10.33581/2520-6508-2020-2-28-35.

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Hausdorff operators on the real line and multidimensional Euclidean spaces originated from some classical summation methods. Now it is an active research area. Hausdorff operators on general groups were defined and studied by the author since 2019. The purpose of this paper is to define and study Hausdorff operators on Lebesgue and real Hardy spaces over homogeneous spaces of locally compact groups. We introduce in particular an atomic Hardy space over homogeneous spaces of locally compact groups and obtain conditions for boundedness of Hausdorff operators on such spaces. Several corollaries a

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14

Bardyla, Serhii, and Alex Ravsky. "Closed subsets of compact-like topological spaces." Applied General Topology 21, no. 2 (2020): 201. http://dx.doi.org/10.4995/agt.2020.12258.

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<p>We investigate closed subsets (subsemigroups, resp.) of compact-like topological spaces (semigroups, resp.). We show that each Hausdorff topological space is a closed subspace of some Hausdorff ω-bounded pracompact topological space and describe open dense subspaces of<br />countably pracompact topological spaces. We construct a pseudocompact topological semigroup which contains the bicyclic monoid as a closed subsemigroup. This example provides an affirmative answer to a question posed by Banakh, Dimitrova, and Gutik in [4]. Also, we show that the semigroup of ω×ω-matrix units

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15

Nayar, Bhamini M. P. "Minimal sequential Hausdorff spaces." International Journal of Mathematics and Mathematical Sciences 2004, no. 22 (2004): 1169–77. http://dx.doi.org/10.1155/s0161171204105012.

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A sequential space(X,T)is called minimal sequential if no sequential topology onXis strictly weaker thanT. This paper begins the study of minimal sequential Hausdorff spaces. Characterizations of minimal sequential Hausdorff spaces are obtained using filter bases, sequences, and functions satisfying certain graph conditions. Relationships between this class of spaces and other classes of spaces, for example, minimal Hausdorff spaces, countably compact spaces, H-closed spaces, SQ-closed spaces, and subspaces of minimal sequential spaces, are investigated. While the property of being sequential

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16

Grainger, Arthur D. "Homeomorphisms of Compact Sets in Certain Hausdorff Spaces." International Journal of Mathematics and Mathematical Sciences 2011 (2011): 1–11. http://dx.doi.org/10.1155/2011/493290.

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We construct a class of Hausdorff spaces (compact and noncompact) with the property that nonempty compact subsets of these spaces that have the same cardinality are homeomorphic. Also, it is shown that these spaces contain compact subsets that are infinite.

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17

Brydun, Viktoriya, and Mykhailo Zarichnyi. "Spaces of max-min measures on compact Hausdorff spaces." Fuzzy Sets and Systems 396 (October 2020): 138–51. http://dx.doi.org/10.1016/j.fss.2019.06.012.

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18

BEZHANISHVILI, GURAM, LEO ESAKIA, and DAVID GABELAIA. "THE MODAL LOGIC OF STONE SPACES: DIAMOND AS DERIVATIVE." Review of Symbolic Logic 3, no. 1 (2010): 26–40. http://dx.doi.org/10.1017/s1755020309990335.

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We show that if we interpret modal diamond as the derived set operator of a topological space, then the modal logic of Stone spaces is K4 and the modal logic of weakly scattered Stone spaces is K4G. As a corollary, we obtain that K4 is also the modal logic of compact Hausdorff spaces and K4G is the modal logic of weakly scattered compact Hausdorff spaces.

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19

Kopperman, Ralph D., and Desmond Robbie. "Skew compact semigroups." Applied General Topology 4, no. 1 (2003): 133. http://dx.doi.org/10.4995/agt.2003.2015.

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<p>Skew compact spaces are the best behaving generalization of compact Hausdorff spaces to non-Hausdorff spaces. They are those (X ; τ ) such that there is another topology τ* on X for which τ V τ* is compact and (X; τ ; τ*) is pairwise Hausdorff; under these conditions, τ uniquely determines τ *, and (X; τ*) is also skew compact. Much of the theory of compact T<sub>2</sub> semigroups extends to this wider class. We show:</p> <p>A continuous skew compact semigroup is a semigroup with skew compact topology τ, such that the semigroup operation is continuous τ<sup

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20

Keesling, James E., and Yuli B. Rudyak. "On fundamental groups of compact Hausdorff spaces." Proceedings of the American Mathematical Society 135, no. 08 (2007): 2629–32. http://dx.doi.org/10.1090/s0002-9939-07-08696-0.

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21

Balogh, Zolt{án T. "On compact Hausdorff spaces of countable tightness." Proceedings of the American Mathematical Society 105, no. 3 (1989): 755. http://dx.doi.org/10.1090/s0002-9939-1989-0930252-6.

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22

Bešlagić, Amer, Eric K. Van Douwen, John W. L. Merrill, and W. Stephen Watson. "The cardinality of countably compact Hausdorff spaces." Topology and its Applications 27, no. 1 (1987): 1–10. http://dx.doi.org/10.1016/0166-8641(87)90053-8.

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23

Keremedis, K., C. Özel, A. Piękosz, Shumrani Al, and E. Wajch. "Compact complement topologies and k-spaces." Filomat 33, no. 7 (2019): 2061–71. http://dx.doi.org/10.2298/fil1907061k.

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Let (X,?) be a Hausdorff space, where X is an infinite set. The compact complement topology ?* on X is defined by: ?* = {0}?{X\M:M is compact in (X,?)}. In this paper, properties of the space (X,?*) are studied in ZF and applied to a characterization of k-spaces, to the Sorgenfrey line, to some statements independent of ZF, as well as to partial topologies that are among Delfs-Knebusch generalized topologies. Between other results, it is proved that the axiom of countable multiple choice (CMC) is equivalent with each of the following two sentences: (i) every Hausdorff first-countable space is

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24

Steprans, Juris, Stephen Watson, and Winfried Just. "A Topological Banach Fixed Point Theorem for Compact Hausdorff Spaces." Canadian Mathematical Bulletin 37, no. 4 (1994): 552–55. http://dx.doi.org/10.4153/cmb-1994-081-0.

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AbstractWe propose an analogue of the Banach contraction principle for connected compact Hausdorff spaces. We define a J-contraction of a connected compact Hausdorff space. We show that every contraction of a compact metric space is a J-contraction and that any J-contraction of a compact metrizable space is a contraction for some admissible metric. We show that every J-contraction has a unique fixed point and that the orbit of each point converges to this fixed point.

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25

Liu, Zeqing, Haiyan Gao, Shin Min Kang, and Yong Soo Kim. "Coincidence and common fixed point theorems in compact Hausdorff spaces." International Journal of Mathematics and Mathematical Sciences 2005, no. 6 (2005): 845–53. http://dx.doi.org/10.1155/ijmms.2005.845.

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The existence of coincidence and fixed points for continuous mappings in compact Hausdorff spaces is established. Some equivalent conditions of the existence of fixed and common fixed points for any continuous mapping and a pair of mappings in compact Hausdorff spaces are given, respectively. Our results extend, improve, and unify the corresponding results due to Jungck, Liu, and Singh and Rao.

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26

Banaschewski, B., and G. C. L. Brummer. "Stably continuous frames." Mathematical Proceedings of the Cambridge Philosophical Society 104, no. 1 (1988): 7–19. http://dx.doi.org/10.1017/s0305004100065208.

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In the lattice theory that underlies topology, that is, in the study of frames, a class of frames arising naturally is that of the stably continuous frames (see §0 for definitions). On the one hand, they correspond to the most reasonable not necessarily Hausdorff compact spaces, and on the other, they are precisely the retracts of coherent frames. Moreover, an important special case of stably continuous frames are the compact regular frames which correspond to compact Hausdorff spaces.

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27

BHATTACHARJEE, PAPIYA. "TWO SPACES OF MINIMAL PRIMES." Journal of Algebra and Its Applications 11, no. 01 (2012): 1250014. http://dx.doi.org/10.1142/s0219498811005373.

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This paper studies algebraic frames L and the set Min (L) of minimal prime elements of L. We will endow the set Min (L) with two well-known topologies, known as the Hull-kernel (or Zariski) topology and the inverse topology, and discuss several properties of these two spaces. It will be shown that Min (L) endowed with the Hull-kernel topology is a zero-dimensional, Hausdorff space; whereas, Min (L) endowed with the inverse topology is a T1, compact space. The main goal will be to find conditions on L for the spaces Min (L) and Min (L)-1 to have various topological properties; for example, comp

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28

SCHNEIDER, FRIEDRICH MARTIN, SEBASTIAN KERKHOFF, MIKE BEHRISCH, and STEFAN SIEGMUND. "LOCALLY COMPACT GROUPS ADMITTING FAITHFUL STRONGLY CHAOTIC ACTIONS ON HAUSDORFF SPACES." International Journal of Bifurcation and Chaos 23, no. 09 (2013): 1350158. http://dx.doi.org/10.1142/s0218127413501587.

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29

Page, Warren. "Compactness and Closedness in Locally Compact Hausdorff Spaces." American Mathematical Monthly 92, no. 7 (1985): 504. http://dx.doi.org/10.2307/2322514.

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30

Page, Warren. "Compactness and Closedness in Locally Compact Hausdorff Spaces." American Mathematical Monthly 92, no. 7 (1985): 504–6. http://dx.doi.org/10.1080/00029890.1985.11971667.

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31

Di Nola, Antonio, Serafina Lapenta, and Ioana LeuŞtean. "Infinitary logic and basically disconnected compact Hausdorff spaces." Journal of Logic and Computation 28, no. 6 (2018): 1275–92. http://dx.doi.org/10.1093/logcom/exy011.

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32

Jayne, J. E., I. Namioka, and C. A. Rogers. "Continuous functions on products of compact Hausdorff spaces." Mathematika 46, no. 2 (1999): 323–30. http://dx.doi.org/10.1112/s0025579300007786.

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33

Bezhanishvili, G., N. Bezhanishvili, T. Santoli, and Y. Venema. "A strict implication calculus for compact Hausdorff spaces." Annals of Pure and Applied Logic 170, no. 11 (2019): 102714. http://dx.doi.org/10.1016/j.apal.2019.06.003.

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34

Shapiro, L. B. "On the homogeneity of dyadic compact Hausdorff spaces." Mathematical Notes 54, no. 4 (1993): 1058–72. http://dx.doi.org/10.1007/bf01210425.

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35

Lu, Hong, and Klaus Weihrauch. "Computable Riesz Representation for Locally Compact Hausdorff Spaces." Electronic Notes in Theoretical Computer Science 202 (March 2008): 3–12. http://dx.doi.org/10.1016/j.entcs.2008.03.002.

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36

Knight, Ronald A. "Iterates of homeomorphisms on locally compact Hausdorff spaces." Topology and its Applications 52, no. 1 (1993): 71–79. http://dx.doi.org/10.1016/0166-8641(93)90092-r.

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37

KANIA, TOMASZ, and RICHARD J. SMITH. "CHAINS OF FUNCTIONS IN -SPACES." Journal of the Australian Mathematical Society 99, no. 3 (2015): 350–63. http://dx.doi.org/10.1017/s1446788715000245.

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The Bishop property (♗), introduced recently by K. P. Hart, T. Kochanek and the first-named author, was motivated by Pełczyński’s classical work on weakly compact operators on $C(K)$-spaces. This property asserts that certain chains of functions in said spaces, with respect to a particular partial ordering, must be countable. There are two versions of (♗): one applies to linear operators on $C(K)$-spaces and the other to the compact Hausdorff spaces themselves. We answer two questions that arose after (♗) was first introduced. We show that if $\mathscr{D}$ is a class of compact spaces that is

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38

Moreno, J. P. "Semicontinuous functions and convex sets in C(K) spaces." Journal of the Australian Mathematical Society 82, no. 1 (2007): 111–21. http://dx.doi.org/10.1017/s1446788700017493.

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AbstractThe stability properties of the family ℳ of all intersections of closed balls are investigated in spaces C(K), where K is an arbitrary Hausdorff compact space. We prove that ℳ is stable under Minkowski addition if and only if K is extremally disconnected. In contrast to this, we show that ℳ is always ball stable in these spaces. Finally, we present a Banach space (indeed a subspace of C[0, 1]) which fails to be ball stable, answering an open question. Our results rest on the study of semicontinuous functions in Hausdorff compact spaces.

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39

Bankston, Paul. "Co-elementary equivalence for compact Hausdorff spaces and compact abelian groups." Journal of Pure and Applied Algebra 68, no. 1-2 (1990): 11–26. http://dx.doi.org/10.1016/0022-4049(90)90129-6.

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40

Diamond, Phil, and Peter Kloeden. "A note on compact sets in spaces of subsets." Bulletin of the Australian Mathematical Society 38, no. 3 (1988): 393–95. http://dx.doi.org/10.1017/s0004972700027763.

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A simple characterisation is given of compact sets of the space K(X), of nonempty compact subsets of a complete metric space X, with the Hausdorff metric dH. It is used to give a new proof of the Blaschke selection theorem for compact starshaped sets.

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41

WANG, HANFENG, and WEI HE. "A NOTE ON -SPACES." Bulletin of the Australian Mathematical Society 90, no. 1 (2014): 144–48. http://dx.doi.org/10.1017/s0004972714000112.

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AbstractIn this paper, it is shown that every compact Hausdorff $K$-space has countable tightness. This result gives a positive answer to a problem posed by Malykhin and Tironi [‘Weakly Fréchet–Urysohn and Pytkeev spaces’, Topology Appl.104 (2000), 181–190]. We show that a semitopological group $G$ that is a $K$-space is first countable if and only if $G$ is of point-countable type. It is proved that if a topological group $G$ is a $K$-space and has a locally paracompact remainder in some Hausdorff compactification, then $G$ is metrisable.

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42

Kovár, Martin Maria. "The Classes of Mutual Compactificability." International Journal of Mathematics and Mathematical Sciences 2007 (2007): 1–11. http://dx.doi.org/10.1155/2007/16135.

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Two disjoint topological spacesX,Yare mutually compactificable if there exists a compact topology onK=X∪Ywhich coincides onX,Ywith their original topologies such that the pointsx∈X,y∈Yhave disjoint neighborhoods inK. The main problem under consideration is the following: which spacesX,Yare so compatible such that they together can form the compact spaceK? In this paper we define and study the classes of spaces with the similar behavior with respect to the mutual compactificability. Two spacesX1,X2belong to the same class if they can substitute each other in the above construction with any spac

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43

Cambern, Michael. "A Banach–Stone theorem for spaces of weak* continuous functions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 101, no. 3-4 (1985): 203–6. http://dx.doi.org/10.1017/s0308210500020771.

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SynopsisIf X is a compact Hausdorff space and E a dual Banach space, let C(X, Eσ*) denote the Banach space of continuous functions F from X to E when the latter space is provided with its weak * topology, normed by . It is shown that if X and Y are extremally disconnected compact Hausdorff spaces and E is a uniformly convex Banach space, then the existence of an isometry between C(X, Eσ*) and C(Y, Eσ*) implies that X and Y are homeomorphic.

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44

Das, T. K. "On projective lift and orbit spaces." Bulletin of the Australian Mathematical Society 50, no. 3 (1994): 445–49. http://dx.doi.org/10.1017/s0004972700013551.

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By constructing the projective lift of a dp-epimorphism, we find a covariant functor E from the category Cd of regular Hausdorff spaces and continuous dp-epimorphisms to its coreflective subcategory εd consisting of projective objects of Cd We use E to show that E(X/G) is homeomorphic to EX/G whenever G is a properly discontinuous group of homeomorphisms of a locally compact Hausdorff space X and X/G is an object of Cd.

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45

Shah, Sejal, and T. K. Das. "A note on the lattice of density preserving maps." Bulletin of the Australian Mathematical Society 72, no. 1 (2005): 1–6. http://dx.doi.org/10.1017/s000497270003481x.

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We study here the poset DP (X) of density preserving continuous maps defined on a Hausdorff sapce X and show that it is a complete lattice for a compact Hausdorff space without isolated points. We further show that for countably compact T3 spaces X and Y without isolated points, DP (X) and DP (Y) are order isomorphic if and only if X and Y are homeomorphic. Finally, Magill's result on the remainder of a locally compact Hausdorff space is deduced from the relation of DP (X) with posets IP (X) of covering maps and EK (X) of compactifications respectively.

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46

Panchapagesan, T. V., and Shivappa Veerappa Palled. "On vector lattice-valued measures II." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 40, no. 2 (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 mea

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47

Kurbanov, Kh, and S. Yodgarov. "A functor IS in the Category Compact Hausdorff Spaces." Bulletin of Science and Practice 6, no. 3 (2020): 13–22. http://dx.doi.org/10.33619/2414-2948/52/01.

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We construct a space of normed, homogeneous and max-plus-semiadditive functionals and we give its description. Further we establish that the construction of taking of a space of normed, homogeneous and max-plus-semiadditive functionals, forms a normal functor acting in the category of Hausdorff compact spaces and their continuous maps.

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48

Wang, Ya, and Ze-Hua Zhou. "Disjoint hypercyclic weighted translations on locally compact hausdorff spaces." Mathematica Slovaca 69, no. 3 (2019): 647–64. http://dx.doi.org/10.1515/ms-2017-0254.

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Abstract Let G be a locally compact second countable Hausdorff space with a positive regular Borel measure λ, where λ is invariant under a continuous injective mapping φ : G → G. We characterize the disjoint hypercyclicity of finite weighted translations generated by φ acting on the weighted space Lp(G, ω) (1 ≤ p < ∞).

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49

Ismail, M., and A. Szymanski. "On locally compact Hausdorff spaces with finite metrizability number." Topology and its Applications 114, no. 3 (2001): 285–93. http://dx.doi.org/10.1016/s0166-8641(00)00043-2.

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50

Wang, Ya, and Ze-Hua Zhou. "Hypercyclicity of weighted translations on locally compact Hausdorff spaces." Dynamical Systems 36, no. 3 (2021): 507–26. http://dx.doi.org/10.1080/14689367.2021.1931814.

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