Independent form of \((\theta, s)\)-continuous functions in topological spaces. (English) Zbl 1456.54004
Summary: We introduce a new class of almost contra-\(P_\beta \)-continuous functions which is a subclass of the class of almost contra-precontinuous functions [E. Ekici, Bull. Malays. Math. Sci. Soc. (2) 27, No. 1, 53–65 (2004; Zbl 1185.54015)]. This class contains the classes of regular set connected functions, perfectly continuous functions and contra-\(P_\beta \)-continuous functions. It is shown that almost contra-\(P_\beta \)-continuity is independent to \((\theta, s)\)-continuity [J. E. Joseph and M. H. Kwack, Proc. Am. Math. Soc. 80, 341–348 (1980; Zbl 0441.54010)] and contra-precontinuity [S. Jafari and T. Noiri, Bull. Malays. Math. Sci. Soc. (2) 25, No. 2, 115–128 (2002; Zbl 1185.54017)]. Furthermore, we obtain basic properties and preservations theorems for almost contra-\(P_\beta \)-continuity.
MSC:
| 54C08 | Weak and generalized continuity |
Keywords:
almost contra-precontinuous functions; \((\theta, s)\)-continuous functions; almost contra-\(P_\beta \)-continuous functions; \(P_\beta \)-open; topological spaceReferences:
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