Results 1 to 10 of about 103 (87)
Continuous Selections and Extremally Disconnected Spaces
Mathematics, 2023 This paper deals with extremally disconnected spaces and extremally disconnected P-spaces. A space X is said to be extremally disconnected if, for every open subset V of X, the closure of V in X is also an open set.
Manuel Sanchís, Sanchís Manuel
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Compact and extremally disconnected spaces [PDF]
International Journal of Mathematics and Mathematical Sciences, 2004 Viglino defined a Hausdorff topological space to be C-compact if each closed subset of the space is an H-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 an S-set ...
Bhamini M. P. Nayar
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Homogeneous subspaces of products of extremally disconnected spaces [PDF]
Topology and Its Applications, 2020 Homogeneous countably compact spaces $X$ and $Y$ whose product $X\times Y$ is not pseudocompact are constructed. It is proved that all compact subsets of homogeneous subspaces of the third power of an extremally disconnected space are finite. Moreover, under CH, all compact subsets of homogeneous subspaces of any finite power of an extremally ...
Evgenii Reznichenko
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A study of extremally disconnected topological spaces [PDF]
Bulletin of Mathematical Sciences, 2011 Throughout, all spaces are assumed to be Tychonoff. A space \(X\) is \textit{extremally disconnected} (\textit{e.d.}~for short) if open subsets of \(X\) have open closures. Any discrete space is a prototypical example of an e.d.~space, though a plethora of non-discrete extremally disconnected spaces is present in mathematics. Let us just mention a fact
Arhangel’Skii Alexander
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On extremally disconnected topological groups
Topology and Its Applications, 2006 AbstractWe introduce the notion of a partially selective ultrafilter and prove that (a) if G is an extremally disconnected topological group and p is a converging nonprincipal ultrafilter on G containing a countable discrete subset, then p is partially selective, and (b) the existence of a nonprincipal partially selective ultrafilter on a countable set
Yevhen Zelenyuk
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Extremally disconnected spaces, subspaces and retracts
Topology and Its Applications, 1993 There is the problem of a satisfactory characterization of the class \(k\)- ED of compact subspaces of extremally disconnected (ED) spaces. An early conjecture of Choquet -- that \(k\)-ED coincides with the class of compact 0-dimensional \(F\)-spaces -- has been shown by \textit{E. K. van Douwen} and \textit{J. van Mill} [Trans. Am. Math. Soc. 259, 121-
J Vermeer
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A new construction of extremally disconnected topologies
Topology and Its Applications, 1994 A general method of constructing extremally disconnected topologies is presented. This method yields countably compact homogeneous extremally disconnected spaces of any cardinality \(\kappa\) for which \(\kappa^ \omega = \kappa\), and two such spaces whose product is not countably compact.
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On some classes of sets in extremally disconnected spaces
Demonstratio Mathematica, 2011 Abstract In the present paper several characterizations of the classical notion of extremally disconnected spaces are obtained. A few relationships for finite products of extremally disconnected spaces are also studied.
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On some properties of the space of minimal prime ideals of 𝐶𝑐 (𝑋) [PDF]
Categories and General Algebraic Structures with Applications, 2022 In this article we consider some relations between the topological properties of the spaces X and Min(Cc (X)) with algebraic properties of Cc (X). We observe that the compactness of Min(Cc (X)) is equivalent to the von-Neumann regularity of qc (X ...
Zahra Keshtkar +3 more
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The nonexistence of extremally disconnected free topological groups
Topology and Its Applications, 2013 An old question of Arkhangel'skii's asks whether a nondiscrete extremally disconnected topological group can be constructed in \(ZFC\). The author proves that, given a topological space \(X\), if there is an extremally disconnected group topology on the free Boolean group \(B(X)\) which satisfies an additional natural condition, then either \(X\) is a \
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