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\(D^*\)-supercontinuous functions. (English) Zbl 1012.54016
The author introduces the following concept: a function \(f:X\to Y\) between topological spaces \(X\) and \(Y\) is \(D^*\)-supercontinuous if for every \(x\in X\) and for every open set \(V\) containing \(f(x)\) there exists a strongly open \(F_\sigma\)-set \(U\) containing \(x\) such that \(f(U)\subset V\). Basic properties of such functions and their relations to other strong forms of continuity (as strong continuity, perfect continuity, supercontinuity etc.) are studied. Also the behaviour of weak (completely) \(G_\delta\)-regular spaces under these functions is investigated.

MSC:
54C05 Continuous maps
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