Split continuity of functions between topological spaces

Document Type

Article

Publication Title

Filomat

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 points of split continuity 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.

First Page

8689

Last Page

8700

DOI

10.2298/FIL2424689G

Publication Date

1-1-2024

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