Results 41 to 50 of about 116 (102)
A note on pseudocompact spaces [PDF]
Journal of the Australian Mathematical Society, 1979 AbstractIn this note we give several new characterizations of arbitrary pseudocompact spaces, that is spaces characterized by the property that all continuous real-valued functions on the space are bounded.
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Baire spaces, k‐spaces, and some properly hereditary properties
International Journal of Mathematics and Mathematical Sciences, Volume 2005, Issue 22, Page 3697-3701, 2005., 2005 A topological property is properly hereditary property if whenever every proper subspace has the property, the whole space has the property. In this note, we will study some topological properties that are preserved by proper subspaces; in fact, we will study the following topological properties: Baire spaces, second category, sequentially compact ...
Adnan Al-Bsoul
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A note on pseudobounded paratopological groups
Topological Algebra and its Applications, 2014 Let G be a paratopological group. Then G is said to be pseudobounded (resp. ω-pseudobounded) if forevery neighbourhood V of the identity e in G, there exists a natural number n such that G = Vn (resp.we have G = ∪ n∈N Vn).
Lin Fucai, Lin Shou, Sánchez Iván
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Approximation of continuous functions on pseudocompact spaces [PDF]
Proceedings of the American Mathematical Society, 1981 If S * is the family of subrings of C*(X) such that if S E S *, S contains the constant functions and is closed under uniform convergence, then the following are equivalent for a space (X, 5). (a) (X, 5) is pseudocompact. (b) If S E S * functionally separates points and zero sets, S generates (X, 5). (c) If S E S * functionally separates zero sets, S =
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Compact‐calibres of regular and monotonically normal spaces
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 4, Page 209-216, 2002., 2002 A topological space has calibre ω1 (resp., calibre (ω1, ω)) if every point‐countable (resp., point‐finite) collection of nonempty open sets is countable. It has compact‐calibre ω1 (resp., compact‐calibre (ω1, ω)) if, for every family of uncountably many nonempty open sets, there is some compact set which meets uncountably many (resp., infinitely many ...
David W. Mcintyre
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Applied General Topology, 2008 In this note a new class of topological spaces generalizing k-spaces, the pseudo-k-spaces, is introduced and investigated. Particular attention is given to the study of products of such spaces, in analogy to what is already known about k-spaces and quasi-
Anna Maria Miranda
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A PSEUDOCOMPACT TYCHONOFF SPACE THAT IS NOT STAR LINDELÖF [PDF]
Bulletin of the Australian Mathematical Society, 2011 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 ...
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Coloring Cantor sets and resolvability of pseudocompact spaces [PDF]
Commentationes Mathematicae Universitatis Carolinae, 2019 8 ...
Juhász, István +2 more
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An operation on topological spaces
Applied General Topology, 2000 A (binary) product operation on a topological space X is considered. The only restrictions are that some element e of X is a left and a right identity with respect to this multiplication, and that certain natural continuity requirements are satisfied ...
A.V. Arhangelskii
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Profinite direct sums with applications to profinite groups of type ΦR$\Phi _R$
Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.Abstract We show that the ‘profinite direct sum’ is a good notion of infinite direct sums for profinite modules, having properties similar to those of direct sums of abstract modules. For example, the profinite direct sum of projective modules is projective, and there is a Mackey's formula for profinite modules described using these sums.
Jiacheng Tang
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