Displaying similar documents to “On almost countably compact spaces”

On relatively almost countably compact subsets

Yan-Kui Song, Shu-Nian Zheng (2010)

Mathematica Bohemica

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A subset Y of a space X is almost countably compact in X if for every countable cover 𝒰 of Y by open subsets of X , there exists a finite subfamily 𝒱 of 𝒰 such that Y ⊆ ⋃ 𝒱 ¯ . In this paper we investigate the relationship between almost countably compact spaces and relatively almost countably compact subsets, and also study various properties of relatively almost countably compact subsets.

Almost * realcompactness

John J. Schommer, Mary Anne Swardson (2001)

Commentationes Mathematicae Universitatis Carolinae

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We provide a new generalization of realcompactness based on ultrafilters of cozero sets and contrast it with almost realcompactness.

On relatively almost Lindelöf subsets

Yankui Song (2009)

Mathematica Bohemica

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A subspace Y of a space X is almost Lindelöf (strongly almost Lindelöf) in X if for every open cover 𝒰 of X (of Y by open subsets of X ), there exists a countable subset 𝒱 of 𝒰 such that Y ⊆ ⋃ { V ¯ V ∈ 𝒱 } . In this paper we investigate the relationships between relatively almost Lindelöf subset and relatively strongly almost Lindelöf subset by giving some examples, and also study various properties of relatively almost Lindelöf subsets and relatively strongly almost Lindelöf subsets.