Characterizations of Strongly Compact Spaces

Abstract

A topological space(X,τ)is said to be strongly compact if every preopen cover of(X,τ)admits a finite subcover. In this paper, we introduce a new class of sets called -preopen sets which is weaker than both open sets and -open sets. Where a subsetAis said to be -preopen if for eachx∈Athere exists a preopen setUxcontainingxsuch thatUx−Ais a finite set. We investigate some properties of the sets. Moreover, we obtain new characterizations and preserving theorems of strongly compact spaces.