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Almost contra-\(P_S\)-continuity in topological spaces. (English) Zbl 1449.54023

There is a part of general topology that deals with the study of different variants of contra-continuity. These studies were initiated by Dontchev, who in 1996 defined contra-continuous functions as such \(f:X\to Y\) for which \(f^{-1}(V)\) is closed in \(X\) for every open set \(V\) in \(Y\), see J. Dontchev [Int. J. Math. Math. Sci. 19, No. 2, 303–310 (1996; Zbl 0840.54015)]. In the paper under review the authors introduce a new property of such type, namely the almost contra-\(P_S\)-continuity. Let \(X\) and \(Y\) be topological spaces. A function \(f:X\to Y\) is called almost contra-\(P_S\)-continuous if \(f^{-1}(V)\) is \(P_S\)-closed in \(X\) for each regular open set \(V\) of \(Y\). From the Introduction: “The paper is organized as follows. Section 2 develops the necessary preliminaries. In Section 3, the concept of almost contra-\(P_S\)-continuity is introduced, and we obtain characterization and basic properties of this notion. In Section 4, separation axioms are studied in relation to almost contra-\(P_S\)-continuity. In Section 5, \(P_S\)-closed graph of almost contra-\(P_S\)-continuous functions are defined. Section 6 gives sufficient conditions for a space to be connected and hyperconnected.”

MSC:

54C08 Weak and generalized continuity
54C10 Special maps on topological spaces (open, closed, perfect, etc.)

Citations:

Zbl 0840.54015
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