On almost countably compact spaces

Abstract

A space $X$ is {ıt 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 $\bigcup\{\overline{V}:Vın \cal V\}=X$. In this paper, weinvestigate the relationship between almost countably compact spacesand countably compact spaces, and also study topological properties of almost countably compact spaces.