Relatively absolutely countably compact spaces.
Song, Yankui (2006)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Displaying similar documents to “On relative -starLindelöfness.”
Relatively absolutely countably compact spaces.
Vietoris topology on spaces dominated by second countable ones
Carlos Islas, Daniel Jardon (2015)
Open Mathematics
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For a given space X let C(X) be the family of all compact subsets of X. A space X is dominated by a space M if X has an M-ordered compact cover, this means that there exists a family F = FK : K ∈ C(M) ⊂ C(X) such that ∪ F = X and K ⊂ L implies that FK ⊂ FL for any K;L ∈ C(M). A space X is strongly dominated by a space M if there exists an M-ordered compact cover F such that for any compact K ⊂ X there is F ∈ F such that K ⊂ F . Let K(X) D C(X){Øbe the set of all nonempty compact subsets...
A note on the extent of two subclasses of star countable spaces
Zuoming Yu (2012)
Open Mathematics
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We prove that every Tychonoff strongly monotonically monolithic star countable space is Lindelöf, which solves a question posed by O.T. Alas et al. We also use this result to generalize a metrization theorem for strongly monotonically monolithic spaces. At the end of this paper, we study the extent of star countable spaces with k-in-countable bases, k ∈ ℤ.
Tychonoff spaces that have a compactification with countable remainder
Henriksen, Melvin
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On the extent of star countable spaces
Ofelia Alas, Lucia Junqueira, Jan Mill, Vladimir Tkachuk, Richard Wilson (2011)
Open Mathematics
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For a topological property P, we say that a space X is star Pif for every open cover Uof the space X there exists Y ⊂ X such that St(Y,U) = X and Y has P. We consider star countable and star Lindelöf spaces establishing, among other things, that there exists first countable pseudocompact spaces which are not star Lindelöf. We also describe some classes of spaces in which star countability is equivalent to countable extent and show that a star countable space with a dense σ-compact subspace...
Remarks on absolutely star countable spaces
Yan-Kui Song (2013)
Open Mathematics
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We prove the following statements: (1) every Tychonoff linked-Lindelöf (centered-Lindelöf, star countable) space can be represented as a closed subspace in a Tychonoff pseudocompact absolutely star countable space; (2) every Hausdorff (regular, Tychonoff) linked-Lindelöf space can be represented as a closed G δ-subspace in a Hausdorff (regular, Tychonoff) absolutely star countable space; (3) there exists a pseudocompact absolutely star countable Tychonoff space having a regular closed...
A countably compact, separable space which is not absolutely countably compact
Jerry E. Vaughan (1995)
Commentationes Mathematicae Universitatis Carolinae
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We construct a space having the properties in the title, and with the same technique, a countably compact topological group which is not absolutely countably compact.