On almost star σ-compact spaces

Abstract

A space X is almost star σ-compact (weakly star σ-compact) if for each
open cover U of X, there exists a σ-compact subset F of X such that
. In this paper, we investigate the relationships among
star σ-compact spaces, almost star σ-compact spaces and weakly star σ-compact
spaces, and also study topological properties of almost star σ-compact spaces.
Mathematics Subject Classification (2010): 54D20, 54C10.