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Insertion of a contra-continuous function between two comparable contra-\( \alpha\)-continuous (contra-\(C\)-continuous) functions. (English) Zbl 1474.54060

Summary: A necessary and sufficient condition in terms of lower cut sets are given for the insertion of a contra-continuous function between two comparable real-valued functions on such topological spaces that kernel of sets are open.

MSC:

54C08 Weak and generalized continuity
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
54C50 Topology of special sets defined by functions
26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
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