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Characterizations of strongly compact spaces. (English) Zbl 1179.54037
Summary: A topological space \((X,\tau)\) is said to be strongly compact if every preopen cover of \((X,\tau)\) admits a finite subcover. In this paper, we introduce a new class of sets called \({\mathcal N}\)-preopen sets which is weaker than both open sets and \({\mathcal N}\)-open sets. Where a subset \(A\) is said to be \({\mathcal N}\)-preopen if for each \(x\in A\) there exists a preopen set \({\mathcal U}_x\) containing \(x\) such that \({\mathcal U}_x - A\) is a finite set. We investigate some properties of the sets. Moreover, we obtain new characterizations and preserving theorems of strongly compact spaces.

54D30 Compactness
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