Characterizations of Strongly Compact Spaces

الملخص EN

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.