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On pre-Urysohn spaces.

Paul, Ramprasad, Bhattacharyya, P. (1999)

Bulletin of the Malaysian Mathematical Society. Second Series

On pseudocompactness and related notions in ZF

Kyriakos Keremedis (2018)

Commentationes Mathematicae Universitatis Carolinae

We study in ZF and in the class of T 1 spaces the web of implications/ non-implications between the notions of pseudocompactness, light compactness, countable compactness and some of their ZFC equivalents.

On pseudo-radial spaces

Aleksander V. Arhangel'skii, Romano Isler, Gino Tironi (1986)

Commentationes Mathematicae Universitatis Carolinae

On relatively almost countably compact subsets

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

Mathematica Bohemica

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.

On relatively almost Lindelöf subsets

Yankui Song (2009)

Mathematica Bohemica

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.

On remote points, non-normality and π -weight ω 1

Sergei Logunov (2001)

Commentationes Mathematicae Universitatis Carolinae

We show, in particular, that every remote point of X is a nonnormality point of β X if X is a locally compact Lindelöf separable space without isolated points and π w ( X ) ω 1 .

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