On strongly \(\theta\)-semi-continuous functions
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.
strongly \(\theta\)-semicontinuous functions
scientific article; zbMATH DE number 1283842