# Between continuity and set connectedness

## DOI:

https://doi.org/10.4995/agt.2010.1727## Keywords:

Almost continuous function, D-continuous function, z-continuous function, Quasi θ-continuous function, Faintly continuous function, Functionally Hausdorff space, Zero set## 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 Dâˆ—-continuous functions, D-continuous function and set connected functions.### Downloads

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*Appl. Gen. Topol.*, vol. 11, no. 1, pp. 43–55, Apr. 2010.

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