Split Continuity of Functions between Topological Spaces

Abstract

In this article, we introduce the notion of split continuity of functions between topological spaces. Also, we give various characterizations of such functions and establish some basic properties. We observe that a function is continuous if and only if it is split continuous and has a closed graph. Furthermore, we study the set of split continuity points of a quasi-continuous function, and we show that the set of all points of split continuity of a quasi-continuous function from a Baire space X into Y contains a dense Gδ subset of X, where Y is Hausdorff and has some additional properties.