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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 $Y \subseteq \bar{⋃ 𝒱}$ . 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.

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