On \(\alpha\)-quasi-irresolute functions (Q2504733)

The authors define a map \(f:X\to Y\) between topological spaces to be \(\alpha\)-quasi-irresolute if for every \(x\in X\) and \(V\subset Y\) with \(f(x)\in V\) and \(G\subset V\subset \overline{G}\) for some open \(G\), there is a \(U\subset X\) with \(x\in U, U\subset \text{Int}\overline{\text{Int}(U)}\) such that \(f(U)\subset\overline{V}\). Properties of that kind of continuity is studied.