Between continuity and set connectedness

J.K. Kohli, D. Singh, Rajesh Kumar, Jeetendra Aggarwal

Abstract

Two new weak variants of continuity called 'R-continuity'and 'F-continuity' are introduced. Their basic properties are studied and their place in the hierarchy of weak variants of continuity, that already exist in the literature, is elaborated. The class of R-continuous functions properly contains the class of continuous functions and is strictly contained in each of the three classes of (1) faintly continu-ous functions studied by Long and Herrignton (Kyungpook Math. J.22(1982), 7-14); (2) D-continuous functions introduced by Kohli (Bull.Cal. Math. Soc. 84 (1992), 39-46), and (3) F-continuous functions which in turn are strictly contained in the class of z-continuous functions studied by Singal and Niemse (Math. Student 66 (1997), 193-210).So the class of R-continuous functions is also properly contained in each of the classes of D∗-continuous functions, D-continuous function and set connected functions.

Keywords

Almost continuous function; D-continuous function; z-continuous function; Quasi θ-continuous function; Faintly continuous function; Functionally Hausdorff space; Zero set

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1. Pseudo perfectly continuous functions and closedness/compactness of their function spaces
J.K. Kohli, D. Singh, Jeetendra Aggarwal, Manoj Rana
Applied General Topology  vol: 14  issue: 1  year: 2013  
doi: 10.4995/agt.2013.1622



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