Between continuity and set connectedness

• Main Authors: J.K. Kohli, D. Singh, Rajesh Kumar, Jeetendra Aggarwal
• Format: Article
• Language: English
• Published: Universitat Politècnica de València 2010-04-01
• Series: Applied General Topology
• Subjects: Almost continuous function; D-continuous function; z-continuous function; Quasi θ-continuous function; Faintly continuous function; Functionally Hausdorff space; Zero set
• Online Access: http://polipapers.upv.es/index.php/AGT/article/view/1727
• ISSN: 1576-9402; 1989-4147

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.