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Weakly contra-\(\beta\)-continuous functions and strongly \(S\beta\)-closed sets. (English) Zbl 1270.54023

Summary: A new form of contra-\(\beta\)-continuity, called weak contra-\(\beta\)-continuity, is introduced. We show that this class of function is weaker than most forms of \(\beta\)-continuity and contra-continuity, but that the class still has interesting properties. The notion of a strongly \(S\beta\)-closed space is defined and conditions are established under which the weakly contra-\(\beta\)-continuous image of a strongly \(S\beta\)-closed space is compact. Various properties of strongly \(S\beta\)-closed spaces are investigated. For example, we show that every strongly \(S\beta\)-closed is the \(\beta\)-closure of a finite set.

MSC:

54C10 Special maps on topological spaces (open, closed, perfect, etc.)
54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.)
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