On $\Gamma$-Paracompact Spaces

Abstract

We introduce the class of $\Gamma$-paracompact spaces as a stronger form of paracompactness. A space $X$ is said to be $\Gamma$-paracompact ($\Gamma$-P, for short) space if every open cover of $X$ has a strongly locally finite (SLF) open refinement. We give some characterizations of $\Gamma$-P spaces. We also define some weaker forms of $\Gamma$-P spaces as $\Gamma_{\sigma}$-paracompact and feebly $\Gamma$-P spaces We later introduce $\Gamma$-expandable spaces and study the relationships between $\Gamma$-expandable and $\Gamma$-P spaces. We also investigate some of topological properties of $\Gamma$-P spaces.