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On strongly \(\theta\)-semi-continuous functions. (English) Zbl 0917.54017

For \((X,\tau)\) a topological space, a subset \(A\) of \(X\) is said to be semi-open if \(A\subset\text{Cl}(\text{Int}(A))\). The complement of a semi-open set is called semi-closed. The intersection of all semi-closed sets containing \(A\) is called the semi-closure of \(A\) and is denoted by \(\text{sCl} (A)\). In this paper the authors introduce a new class of functions called strongly \(\theta\)-semi-continuous functions. A function \(f:X\to Y\) is said to be strongly \(\theta\)-semicontinuous, if for each \(x\in X\) and each open set \(V\) in \(Y\) containing \(f(x)\) there exists a semi-open set \(U\) in \(X\) containing \(x\) such that \(f(\text{sCl}(U))\subset V\). The authors obtain their characterizations and some of their fundamental properties.
Reviewer: V.Popa (Bacau)

MSC:

54C08 Weak and generalized continuity
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