Displaying similar documents to “Small subsets of first countable spaces”

Remarks on star countable discrete closed spaces

Yan-Kui Song (2013)

Czechoslovak Mathematical Journal

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In this paper, we prove the following statements: (1) There exists a Tychonoff star countable discrete closed, pseudocompact space having a regular-closed subspace which is not star countable. (2) Every separable space can be embedded into an absolutely star countable discrete closed space as a closed subspace. (3) Assuming 2 ℵ 0 = 2 ℵ 1 , there exists a normal absolutely star countable discrete closed space having a regular-closed subspace which is not star countable.

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...