We introduce the class of S-paracompact spaces as a generalization of paracompact spaces. A space (X, T ) is S-paracompact if every open cover of X has a locally finite semi-open refinement. We characterize S-paracompact spaces and study their basic properties. The relationships between S-paracompact spaces and other well-known spaces are investigated.
IntroductionIn 1963, Levine [7], introduced and studied semi-open sets in topological spaces. Several spaces are defined in terms of semi-open sets such as countably S-closed spaces [5], S-closed spaces [14], s-expandable spaces [1], etc.The purpose of this paper is to introduce and study the class of Sparacompact spaces, characterized by the condition that every open cover of the space has a locally finite semi-open refinement. In Section 2, we provide several characterizations of S-paracompact spaces and investigate the relationship between S-paracompact spaces and paracompact spaces, compact spaces, countably S-closed spaces and S-closed spaces. In Sections 3 and 4 we define αS-paracompact sets and study some basic properties of S-paracompact spaces, i.e. subspaces, sum and product.
PreliminariesThroughout this work a space will always mean a topological space in which no separation axiom is assumed unless explicitly stated. Let (X, T ) be a space and A be a subset of X. The closure of A, the interior of A and the relative topology on A in (X, T ) will be denoted by cl (A), int (A) and T A ,
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