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 subset A is said to be -preopen if for each x∈A there exists a preopen set Ux containing x such that Ux−A is a finite set. We investigate some properties of the sets. Moreover, we obtain new characterizations and preserving theorems of strongly compact spaces.