Abstract

A space $X$ is {\it almost countably compact\/} if for every countable open cover $\cal U$ of $X$, there exists a finite subset $\cal V$ of $\cal U$ such that $\bigcup\{\overline{V}:V\in \cal V\}=X$. In this paper, we investigate the relationship between almost countably compact spaces and countably compact spaces, and also study topological properties of almost countably compact spaces.

Keywords: Compact; countably compact; almost countably compact.

MSC: 54D20, 54D55

Pages:  159$-$165     

Volume  64 ,  Issue  2 ,  2012