On $\\Gamma$-Paracompact Spaces
Authors : Necati Can Açikgöz
Pages : 77-81
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Publication Date : 2023-04-30
Article Type : Research
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.Keywords : paracompact, $\\Gamma$-paracompact, regular open set, strongly locally finite collection