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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
##### Keywords:
supercontinuous function