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\(R_\delta\)-supercontinuous functions. (English) Zbl 1300.54022
Summary: A new class of functions called ‘\(R_\delta\)-supercontinuous functions’ is introduced. Their basic properties are studied and their place in the hierarchy of strong variants of continuity which already exist in the literature is elaborated. The class of \(R_\delta\)-supercontinuous functions properly contains the class of \(R_{z}\)-supercontinuous functions which in its turn properly contains the class of \(R_{cl}\)-supercontinuous functions and so includes all \(R_{cl}\)-supercontinuous (\(\equiv\)clopen continuous) functions and is properly contained in the class of \(R\)-supercontinuous functions.

MSC:
54C08 Weak and generalized continuity
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.)
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
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