Relatively Absolutely Countably Compact Spaces

Song,Y.K., (2006) Relatively Absolutely Countably Compact Spaces. Bulletin of the Malaysian Mathematical Sciences Society, 29 (1). pp. 17-21. ISSN 0126-6705

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Official URL: http://math.usm.my/bulletin/pdf/v29n1/v29n1p3.pdf

Affiliations

Nanjing Normal University, Dept. of Mathematics

Abstract

A subspace $Y$ of a space $X$ is $absolutely$ $countably$ $compact$ $(=acc)$ $(strongly$ $absolutely$ $countably$ $compact(=strongly$ $acc))$ in $X$ if for every open cover $\mathcal{U}$ of $X$ and every dense subspace $D \subseteq X$ (respectively, $D \subseteq Y$ ) there exists a finite subset $F \subseteq D$ such that $Y \subseteq St(F,\mathcal{U})$ , where $St(F,\mathcal{U})=\bigcup \{ U\in \mathcal{U}:U\cap F\neq \emptyset \}$ . In this paper, we investigate the relationships between these spaces and other starcompact spaces by giving some examples, and also study topological properties of relatively absolutely countably compact spaces.