Results 21 to 30 of about 116 (111)
New characterisations of pseudocompact spaces [PDF]
Bulletin of the Australian Mathematical Society, 1988 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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A characterization of pseudocompactness
International Journal of Mathematics and Mathematical Sciences, 1981 It is proved here that a completely regular Hausdorff space X is pseudocompact if and only if for any continuous function f from X to a pseudocompact space (or a compact space) Y, f*ϕ is z-ultrafilter whenever ϕ is a z-ultrafilter on X.
Prabduh Ram Misra, Vinodkumar
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Selectively Pseudocompact Groups without Infinite Separable Pseudocompact Subsets
Axioms, 2018 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 ...
Dmitri Shakhmatov, Víctor Hugo Yañez
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On weaker forms of compactness Lindelöfness and countable compactness
International Journal of Mathematics and Mathematical Sciences, 1990 A theory of e-countable compactness and e-Lindelöfness which are weaker than the concepts of countable compactness and Lindelöfness respectively is developed.
D. Baboolal, J. Backhouse, R. G. Ori
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Topology and its Applications, 1998 The paper is full of interesting results on pseudocompact spaces. The main result generalizes Comfort-Ross theorems [\textit{W. W. Comfort} and \textit{K. A. Ross}, Pac. J. Math. 16, 483-496 (1966; Zbl 0214.28502)]: (1) Every product of pseudocompact Mal'tsev spaces is pseudocompact; (2) If \(X\) is a pseudocompact Mal'tsev space, then every Mal'tsev ...
Reznichenko, E.A., Uspenskij, V.V.
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The equivalence of two definitions of sequential pseudocompactness
Applied General Topology, 2016 We show that two possible definitions of sequential pseudocompactness are equivalent, and point out some consequences.
Paolo Lipparini
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Free Subspaces of Free Locally Convex Spaces
Journal of Function Spaces, Volume 2018, Issue 1, 2018., 2018 If X and Y are Tychonoff spaces, let L(X) and L(Y) be the free locally convex space over X and Y, respectively. For general X and Y, the question of whether L(X) can be embedded as a topological vector subspace of L(Y) is difficult. The best results in the literature are that if L(X) can be embedded as a topological vector subspace of L(I), where I=[0 ...
Saak S. Gabriyelyan +2 more
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Periodic Solutions and S‐Asymptotically Periodic Solutions to Fractional Evolution Equations
Discrete Dynamics in Nature and Society, Volume 2017, Issue 1, 2017., 2017 This paper deals with the existence and uniqueness of periodic solutions, S‐asymptotically periodic solutions, and other types of bounded solutions for some fractional evolution equations with the Weyl‐Liouville fractional derivative defined for periodic functions. Applying Fourier transform we give reasonable definitions of mild solutions.
Jia Mu, Yong Zhou, Li Peng, Can Li
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On nearly pseudocompact spaces
Topology and its Applications, 1980 AbstractA completely regular space X is called nearly pseudocompact if υX−X is dense in βX−X, where βX is the Stone-Čech compactification of X and υX is its Hewitt realcompactification. After characterizing nearly pseudocompact spaces in a variety of ways, we show that X is nearly pseudocompact if it has a dense locally compact pseudocompact subspace ...
Henriksen, Melvin, Rayburn, Marlon C.
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Brandt Extensions and Primitive Topological Inverse Semigroups
International Journal of Mathematics and Mathematical Sciences, Volume 2010, Issue 1, 2010., 2010 We study (countably) compact and (absolutely) H‐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.
Tetyana Berezovski +3 more
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