Journal articles: 'Pseudocompact space'

1

Watson, Stephen. "A connected pseudocompact space." Topology and its Applications 57, no. 2-3 (1994): 151–62. http://dx.doi.org/10.1016/0166-8641(94)90047-7.

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2

Yan-Min, Wang. "New characterisations of pseudocompact spaces." Bulletin of the Australian Mathematical Society 38, no. 2 (1988): 293–98. http://dx.doi.org/10.1017/s0004972700027568.

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In this paper, we give a new characterisation of pseudo-compact spaces, namely a space X is pseudocompact if and only if each σ-point finite open cover of X has a finite subfamily whose union is dense. As a corollary, we show that every pseudocompact σ-metacompact (or screenable) space is compact, which sharpens some known results.

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3

Pavlov, O. I. "LINEARLY ORDERED SPACE WHOSE SQUARE AND HIGHER POWERS CANNOT BE CONDENSED ONTO A NORMAL SPACE." Vestnik of Samara University. Natural Science Series 20, no. 10 (2017): 68–73. http://dx.doi.org/10.18287/2541-7525-2014-20-10-68-73.

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One of the central tasks in the theory of condensations is to describe topological properties that can be improved by condensation (i.e. a continuous one-to-one mapping). Most of the known counterexamples in the ﬁeld deal with non-hereditary properties. We construct a countably compact linearly ordered (hence, monotonically normal, thus ” very strongly” hereditarily normal) topological space whose square and higher powers cannot be condensed onto a normal space. The constructed space is necessarily pseudocompact in all the powers, which complements a known result on condensations of non-pseudocompact spaces.

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4

Bella, Angelo. "Few remarks on maximal pseudocompactness." Applied General Topology 19, no. 1 (2018): 155. http://dx.doi.org/10.4995/agt.2018.7888.

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A pseudocompact space is maximal pseudocompact if every strictly finer topology is no longer pseudocompact. The main result here is a counterexample which answers a question rised by Alas, Sanchis and Wilson.

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5

Shakhmatov, Dmitri, and Víctor Yañez. "Selectively Pseudocompact Groups without Infinite Separable Pseudocompact Subsets." Axioms 7, no. 4 (2018): 86. http://dx.doi.org/10.3390/axioms7040086.

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We give a “naive” (i.e., using no additional set-theoretic assumptions beyond ZFC, the Zermelo-Fraenkel axioms of set theory augmented by the Axiom of Choice) example of a Boolean topological group G without infinite separable pseudocompact subsets having the following “selective” compactness property: For each free ultrafilter p on the set N of natural numbers and every sequence ( U n ) of non-empty open subsets of G, one can choose a point x n ∈ U n for all n ∈ N in such a way that the resulting sequence ( x n ) has a p-limit in G; that is, { n ∈ N : x n ∈ V } ∈ p for every neighbourhood V of x in G. In particular, G is selectively pseudocompact (strongly pseudocompact) but not selectively sequentially pseudocompact. This answers a question of Dorantes-Aldama and the first listed author. The group G above is not pseudo- ω -bounded either. Furthermore, we show that the free precompact Boolean group of a topological sum ⨁ i ∈ I X i , where each space X i is either maximal or discrete, contains no infinite separable pseudocompact subsets.

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6

Baboolal, D., J. Backhouse, and R. G. Ori. "On weaker forms of compactness Lindelöfness and countable compactness." International Journal of Mathematics and Mathematical Sciences 13, no. 1 (1990): 55–59. http://dx.doi.org/10.1155/s0161171290000084.

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A theory of e-countable compactness and e-Lindelöfness which are weaker than the concepts of countable compactness and Lindelöfness respectively is developed. Amongst other results we show that an e-countably compact space is pseudocompact, and an example of a space which is pseudocompact but not e-countably compact with respect to any dense set is presented. We also show that every e-Lindelöf metric space is separable.

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7

van Mill, Jan. "Every crowded pseudocompact ccc space is resolvable." Topology and its Applications 213 (November 2016): 127–34. http://dx.doi.org/10.1016/j.topol.2016.08.020.

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8

Künzi, Hans-Peter A. "A note on uniform ordered spaces." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 42, no. 3 (1987): 349–52. http://dx.doi.org/10.1017/s1446788700028627.

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AbstractWe characterize the generalized ordered topological spaces X for which the uniformity (X) is convex. Moreover, we show that a uniform ordered space for which every compatible convex uniformity is totally bounded, need not be pseudocompact.

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9

Mitra, Biswajit, and Debojyoti Chowdhury. "Ideal spaces." Applied General Topology 22, no. 1 (2021): 79. http://dx.doi.org/10.4995/agt.2021.13608.

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Let C∞ (X) denote the family of real-valued continuous functions which vanish at infinity in the sense that {x ∈ X : |f(x)| ≥ 1/n} is compact in X for all n ∈ N. It is not in general true that C∞ (X) is an ideal of C(X). We define those spaces X to be ideal space where C∞ (X) is an ideal of C(X). We have proved that nearly pseudocompact spaces are ideal spaces. For the converse, we introduced a property called “RCC” property and showed that an ideal space X is nearly pseudocompact if and only if X satisfies ”RCC” property. We further discussed some topological properties of ideal spaces.

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10

Good, Chris, and A. M. Mohamad. "A metrisation theorem for pseudocompact spaces." Bulletin of the Australian Mathematical Society 63, no. 1 (2001): 101–4. http://dx.doi.org/10.1017/s0004972700019158.

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11

Kaķol, Jerzy, Stephen A. Saxon, and Aaron R. Todd. "THE ANALYSIS OF WARNER BOUNDEDNESS." Proceedings of the Edinburgh Mathematical Society 47, no. 3 (2004): 625–31. http://dx.doi.org/10.1017/s001309150300066x.

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AbstractIn answer to Jarchow’s 1981 text, we recently characterized when $C_{\textrm{c}}(X)$ is a $df$-space, finding along the way attractive analytic characterizations of when the Tychonov space $X$ is pseudocompact. Analogues now reveal how exquisitely Warner boundedness lies between these two notions. To illustrate, $X$ is pseudocompact, $X$ is Warner bounded or $C_{\textrm{c}}(X)$ is a $df$-space if and only if for each sequence $(\mu_{n})_{n}\subset C_{\textrm{c}}(X)'$ there exists a sequence $(\varepsilon_{n})_{n}\subset(0,1]$ such that $(\varepsilon_{n}\mu_{n})_{n}$ is weakly bounded, is strongly bounded or is equicontinuous, respectively. Our characterizations and proofs add to and simplify Warner’s.AMS 2000 Mathematics subject classification: Primary 46A08; 46A30; 54C35

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12

SONG, YANKUI. "A PSEUDOCOMPACT TYCHONOFF SPACE THAT IS NOT STAR LINDELÖF." Bulletin of the Australian Mathematical Society 84, no. 3 (2011): 452–54. http://dx.doi.org/10.1017/s0004972711002413.

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AbstractLet P be a topological property. A space X is said to be star P if whenever 𝒰 is an open cover of X, there exists a subspace A⊆X with property P such that X=St(A,𝒰), where St(A,𝒰)=⋃ {U∈𝒰:U∩A≠0̸}. In this paper we construct an example of a pseudocompact Tychonoff space that is not star Lindelöf, which gives a negative answer to Alas et al. [‘Countability and star covering properties’, Topology Appl.158 (2011), 620–626, Question 3].

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13

Watson, W. Stephen. "A pseudocompact meta-lindeöf space which is not compact." Topology and its Applications 20, no. 3 (1985): 237–43. http://dx.doi.org/10.1016/0166-8641(85)90091-4.

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14

Song, Yan-Kui. "Remarks on neighborhood star-Lindelöf spaces II." Filomat 27, no. 5 (2013): 875–80. http://dx.doi.org/10.2298/fil1305875s.

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A space X is said to be neighborhood star-Lindel?f if for every open cover U of X there exists a countable subset A of X such that for every open O?A, X=St(O,U). In this paper, we continue to investigate the relationship between neighborhood star-Lindel?f spaces and related spaces, and study topological properties of neighborhood star-Lindel?f spaces in the classes of normal and pseudocompact spaces. .

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15

Pestov, Vladimir. "Free Abelian topological groups and the Pontryagin-Van Kampen duality." Bulletin of the Australian Mathematical Society 52, no. 2 (1995): 297–311. http://dx.doi.org/10.1017/s0004972700014726.

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We study the class of Tychonoff topological spaces such that the free Abelian topological group A(X) is reflexive (satisfies the Pontryagin-van Kampen duality). Every such X must be totally path-disconnected and (if it is pseudocompact) must have a trivial first cohomotopy group π1(X). If X is a strongly zero-dimensional space which is either metrisable or compact, then A(X) is reflexive.

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16

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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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 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 cannot be embedded into a Hausdorff topological semigroup whose space is weakly H-closed.

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17

Rodrigues, Vinicius de Oliveira, and Artur Hideyuki Tomita. "Small MAD families whose Isbell--Mr\'owka space has pseudocompact hyperspace." Fundamenta Mathematicae 247, no. 1 (2019): 99–108. http://dx.doi.org/10.4064/fm657-10-2018.

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18

DUBE, THEMBA. "A NOTE ON RELATIVE PSEUDOCOMPACTNESS IN THE CATEGORY OF FRAMES." Bulletin of the Australian Mathematical Society 87, no. 1 (2012): 120–30. http://dx.doi.org/10.1017/s000497271200024x.

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AbstractA subspace S of Tychonoff space X is relatively pseudocompact in X if every f∈C(X) is bounded on S. As is well known, this property is characterisable in terms of the functor υ which reflects Tychonoff spaces onto the realcompact ones. A device which exists in the category CRegFrm of completely regular frames which has no counterpart in Tych is the functor which coreflects completely regular frames onto the Lindelöf ones. In this paper we use this functor to characterise relative pseudocompactness.

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19

Kim, Junhui. "A non-2-starcompact, pseudocompact Tychonoff space whose hyperspace is 2-starcompact." Topology and its Applications 160, no. 1 (2013): 126–32. http://dx.doi.org/10.1016/j.topol.2012.10.009.

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20

Baboolal, D. "Local Connectedness of the stone-Čech Compactification." Canadian Mathematical Bulletin 31, no. 2 (1988): 236–40. http://dx.doi.org/10.4153/cmb-1988-036-2.

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AbstractA uniform space X is said to be uniformly locally connected if given any entourage U there exists an entourage V ⊂ U such that V[x] is connected for each x ∈ X. It is said to have property S if given any entourage U, X can be written as a finite union of connected sets each of which is U-small.Based on these two uniform connection properties, another proof is given of the following well known result in the theory of locally connected spaces: The Stone-Čech compactification βX is locally connected if and only if X is locally connected and pseudocompact.

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21

Abu Osba, Emad A. "Purity of the ideal of continuous functions with pseudocompact support." International Journal of Mathematics and Mathematical Sciences 29, no. 7 (2002): 381–88. http://dx.doi.org/10.1155/s0161171202011067.

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LetCΨ(X)be the ideal of functions with pseudocompact support and letkXbe the set of all points inυXhaving compact neighborhoods. We show thatCΨ(X)is pure if and only ifβX−kXis a round subset ofβX,CΨ(X)is a projectiveC(X)-module if and only ifCΨ(X)is pure andkXis paracompact. We also show that ifCΨ(X)is pure, then for eachf∈CΨ(X)the ideal(f)is a projective (flat)C(X)-module if and only ifkXis basically disconnected (F′-space).

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Abu Osba, E. A., and H. Al-Ezeh. "Some properties of the ideal of continuous functions with pseudocompact support." International Journal of Mathematics and Mathematical Sciences 27, no. 3 (2001): 169–76. http://dx.doi.org/10.1155/s0161171201010389.

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LetC(X)be the ring of all continuous real-valued functions defined on a completely regularT1-space. LetCΨ(X)andCK(X)be the ideal of functions with pseudocompact support and compact support, respectively. Further equivalent conditions are given to characterize when an ideal ofC(X)is aP-ideal, a concept which was originally defined and characterized by Rudd (1975). We used this new characterization to characterize whenCΨ(X)is aP-ideal, in particular we proved thatCK(X)is aP-ideal if and only ifCK(X)={f∈C(X):f=0except on a finite set}. We also used this characterization to prove that for any idealIcontained inCΨ(X),Iis an injectiveC(X)-module if and only ifcoz Iis finite. Finally, we showed thatCΨ(X)cannot be a proper prime ideal whileCK(X)is prime if and only ifXis an almost compact noncompact space and∞is anF-point. We give concrete examples exemplifying the concepts studied.

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23

Osipov, Alexander V. "The Menger and projective Menger properties of function spaces with the set-open topology." Mathematica Slovaca 69, no. 3 (2019): 699–706. http://dx.doi.org/10.1515/ms-2017-0258.

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Abstract For a Tychonoff space X and a family λ of subsets of X, we denote by Cλ(X) the space of all real-valued continuous functions on X with the set-open topology. A Menger space is a topological space in which for every sequence of open covers 𝓤1, 𝓤2, … of the space there are finite sets 𝓕1 ⊂ 𝓤1, 𝓕2 ⊂ 𝓤2, … such that family 𝓕1 ∪ 𝓕2 ∪ … covers the space. In this paper, we study the Menger and projective Menger properties of a Hausdorff space Cλ(X). Our main results state that Cλ(X) is Menger if and only if Cλ(X) is σ-compact; Cp(Y | X) is projective Menger if and only if Cp(Y | X) is σ-pseudocompact where Y is a dense subset of X.

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24

Garrido, M. I., and F. Montalvo. "Uniform density and M−density for subrings of C(X)." Bulletin of the Australian Mathematical Society 49, no. 3 (1994): 427–32. http://dx.doi.org/10.1017/s0004972700016531.

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This paper deals with the equivalence between u−density and m−density for the subrings of C(X). It was proved by Kurzweil that such equivalence holds for those subrings that are closed under bounded inversion. Here an example is given in C(N) of a u−dense subring that is not m−dense. It is deduced that the two types of density coincide only in the trivial case where these topologies are the same, that is, if and only if X is a pseudocompact space.

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25

Shakhmatov, D. B. "A pseudocompact Tychonoff space all countable subsets of which are closed and C∗-embedded." Topology and its Applications 22, no. 2 (1986): 139–44. http://dx.doi.org/10.1016/0166-8641(86)90004-0.

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Maslyuchenko, O., and A. Kushnir. "PAIRS OF HAHN AND SEPARATELY CONTINUOUS FUNCTION." Bukovinian Mathematical Journal 9, no. 1 (2021): 210–29. http://dx.doi.org/10.31861/bmj2021.01.18.

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In this paper we continue the study of interconnections between separately continuous function which was started by V. K. Maslyuchenko. A pair (g, h) of functions on a topological space is called a pair of Hahn if g ≤ h, g is an upper semicontinuous function and h is a lower semicontinuous function. We say that a pair of Hahn (g, h) is generated by a function f, which depends on two variables, if the inﬁmum of f and the supremum of f with respect to the second variable equals g and h respectively. We prove that for any perfectly normal space X and non-pseudocompact space Y every pair of Hahn on X is generated by a continuous function on X x Y . We also obtain that for any perfectly normal space X and for any space Y having non-scattered compactiﬁcation any pair of Hahn on X is generated by a separately continuous function on X x Y .

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27

Xie, Li-Hong, and Shou Lin. "A note on the continuity of the inverse in paratopological groups." Studia Scientiarum Mathematicarum Hungarica 51, no. 3 (2014): 326–34. http://dx.doi.org/10.1556/sscmath.51.2014.3.1286.

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The problem when a paratopolgical group (or semitopological group) is a topological group is interesting and important. In this paper, we continue to study this problem. It mainly shows that: (1) Let G be a paratopological group and put τ = ωHs(G); then G is a topological group if G is a Pτ-space; (2) every co-locally countably compact paratopological group G with ωHs(G) ≦ ω is a topological group; (3) every co-locally compact paratopological group is a topological group; (4) each 2-pseudocompact paratopological group G with ωHs(G) ≦ ω is a topological group. These results improve some results in [11, 13].

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28

Ghosh, Partha Pratim, and Biswajit Mitra. "Hard pseudocompact spaces." Quaestiones Mathematicae 35, no. 3 (2012): 313–29. http://dx.doi.org/10.2989/16073606.2012.725272.

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29

Reznichenko, E. A., and V. V. Uspenskij. "Pseudocompact Mal'tsev spaces." Topology and its Applications 86, no. 1 (1998): 83–104. http://dx.doi.org/10.1016/s0166-8641(97)00124-7.

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Lin, Fucai. "Pseudocompact rectifiable spaces." Topology and its Applications 164 (March 2014): 215–28. http://dx.doi.org/10.1016/j.topol.2014.01.007.

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31

Song, Yan-Kui. "Remarks on star covering properties in pseudocompact spaces." Mathematica Bohemica 138, no. 2 (2013): 165–69. http://dx.doi.org/10.21136/mb.2013.143288.

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32

Antonyan, Natella. "On the maximalG-compactification of products of twoG-spaces." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–9. http://dx.doi.org/10.1155/ijmms/2006/93218.

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LetGbe any Hausdorff topological group and letβGXdenote the maximalG-compactification of aG-Tychonoff spaceX. We prove that ifXandYare twoG-Tychonoff spaces such that the productX×Yis pseudocompact, thenβG(X×Y)=βGX×βGX.

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33

Acharyya, Amrita, Sudip Kumar Acharyya, Sagarmoy Bag, and Joshua Sack. "Intermediate rings of complex-valued continuous functions." Applied General Topology 22, no. 1 (2021): 47. http://dx.doi.org/10.4995/agt.2021.13165.

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For a completely regular Hausdorff topological space X, let C(X, C) be the ring of complex-valued continuous functions on X, let C ∗ (X, C) be its subring of bounded functions, and let Σ(X, C) denote the collection of all the rings that lie between C ∗ (X, C) and C(X, C). We show that there is a natural correlation between the absolutely convex ideals/ prime ideals/maximal ideals/z-ideals/z ◦ -ideals in the rings P(X, C) in Σ(X, C) and in their real-valued counterparts P(X, C) ∩ C(X). These correlations culminate to the fact that the structure space of any such P(X, C) is βX. For any ideal I in C(X, C), we observe that C ∗ (X, C)+I is a member of Σ(X, C), which is further isomorphic to a ring of the type C(Y, C). Incidentally these are the only C-type intermediate rings in Σ(X, C) if and only if X is pseudocompact. We show that for any maximal ideal M in C(X, C), C(X, C)/M is an algebraically closed field, which is furthermore the algebraic closure of C(X)/M ∩C(X). We give a necessary and sufficient condition for the ideal CP (X, C) of C(X, C), which consists of all those functions whose support lie on an ideal P of closed sets in X, to be a prime ideal, and we examine a few special cases thereafter. At the end of the article, we find estimates for a few standard parameters concerning the zero-divisor graphs of a P(X, C) in Σ(X, C).

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Arhangel'skii, A. V. "Strongly τ-pseudocompact spaces". Topology and its Applications 89, № 3 (1998): 285–98. http://dx.doi.org/10.1016/s0166-8641(97)00220-4.

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Sánchez-Texis, Fernando, and Oleg Okunev. "Pseudocomplete and weakly pseudocompact spaces." Topology and its Applications 163 (February 2014): 174–80. http://dx.doi.org/10.1016/j.topol.2013.10.016.

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Matveev, M. V. "Closed imbeddings in pseudocompact spaces." Mathematical Notes of the Academy of Sciences of the USSR 41, no. 3 (1987): 217–26. http://dx.doi.org/10.1007/bf01158252.

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Hernández-Hernández, F., R. Rojas-Hernández, and Á. Tamariz-Mascarúa. "Non-trivial non weakly pseudocompact spaces." Topology and its Applications 247 (September 2018): 1–8. http://dx.doi.org/10.1016/j.topol.2018.06.016.

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Sokolovskaya, Aleena. "G-compactifications of pseudocompact G-spaces." Topology and its Applications 155, no. 4 (2008): 342–46. http://dx.doi.org/10.1016/j.topol.2007.06.019.

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39

Song, Yankui. "Star covering properties in pseudocompact spaces." Topology and its Applications 159, no. 5 (2012): 1462–66. http://dx.doi.org/10.1016/j.topol.2012.01.006.

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40

Choban, Mitrofan M. "On paracompactGδ-subspaces of pseudocompact spaces". Topology and its Applications 179 (січень 2015): 62–73. http://dx.doi.org/10.1016/j.topol.2014.08.016.

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41

Romaguera, S., and M. Sanchis. "Continuity of the Inverse in Pseudocompact Paratopological Groups." Algebra Colloquium 14, no. 01 (2007): 167–75. http://dx.doi.org/10.1142/s1005386707000168.

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By a celebrated theorem of Numakura, a Hausdorff compact topological semigroup with two-sided cancellation is a group which has inverse continuous, i.e., it is a topological group. We improve Numakura's Theorem in the realm of non-Hausdorff topological semigroups. This improvement together with some properties of pseudocompact nature in the field of bitopological spaces is used in order to prove that a T0 paratopological group (G,τ) is a (Hausdorff) pseudocompact topological group if and only if (G, τ ∨ τ-1) is pseudocompact or, equivalently, G is Gδ-dense in the Stone–Čech bicompactification [Formula: see text] of (G, τ, τ-1). We also present a version for paratopological groups of the renowned Comfort–Ross Theorem stating that a topological group is pseudocompact if and only if its Stone–Čech compactification is a topological group.

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42

Dow, Alan, Jack R. Porter, R. M. Stephenson, and R. Grant Woods. "Spaces whose Pseudocompact Subspaces are Closed Subsets." Applied General Topology 5, no. 2 (2004): 243. http://dx.doi.org/10.4995/agt.2004.1973.

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43

DOLAS, UDAY. "On Coincidence Points in Pseudocompact Tichonov Spaces." Journal of Ultra Scientist of Physical Sciences Section A 29, no. 03 (2017): 101–3. http://dx.doi.org/10.22147/jusps-a/290301.

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Dikranjan, Dikran, Kazumi Miyazaki, Tsugunori Nogura, and Takamitsu Yamauchi. "On pseudocompact spaces with a weak selection." Topology and its Applications 230 (October 2017): 490–505. http://dx.doi.org/10.1016/j.topol.2017.08.019.

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45

Bella, Angelo, and Oleg I. Pavlov. "Embeddings into pseudocompact spaces of countable tightness." Topology and its Applications 138, no. 1-3 (2004): 161–66. http://dx.doi.org/10.1016/j.topol.2003.03.001.

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TREE, I. J. "Consistently, Must Perfect Pseudocompact Spaces Be Separable?" Annals of the New York Academy of Sciences 704, no. 1 Papers on Gen (1993): 358. http://dx.doi.org/10.1111/j.1749-6632.1993.tb52541.x.

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47

Pelant, Jan, Mihail G. Tkachenko, Vladimir V. Tkachuk, and Richard G. Wilson. "Pseudocompact Whyburn spaces need not be Fréchet." Proceedings of the American Mathematical Society 131, no. 10 (2002): 3257–65. http://dx.doi.org/10.1090/s0002-9939-02-06840-5.

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48

Choban, Mitrofan M. "FRAGMENTABILITY OF FUNCTION SPACES Cp(T) FOR PSEUDOCOMPACT SPACES T." Математички билтен/BULLETIN MATHÉMATIQUE DE LA SOCIÉTÉ DES MATHÉMATICIENS DE LA RÉPUBLIQUE MACÉDOINE, no. 2 (2015): 5–11. http://dx.doi.org/10.37560/matbil1520005ch.

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István, Juhász, Soukup Lajos, and Szentmiklóssy Zoltán. "Coloring Cantor sets and resolvability of pseudocompact spaces." Commentationes Mathematicae Universitatis Carolinae 59, no. 4 (2019): 523–29. http://dx.doi.org/10.14712/1213-7243.2015.261.

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50

Eckertson, Frederick W. "Sums, products, and mappings of weakly pseudocompact spaces." Topology and its Applications 72, no. 2 (1996): 149–57. http://dx.doi.org/10.1016/0166-8641(95)00103-4.

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Journal articles on the topic 'Pseudocompact space'

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