Locally closed sets and LC‐continuous functions

Source abstract

In this paper we introduce and study three different notions of generalized continuity, namely LC‐irresoluteness, LC‐continuity and sub‐LC‐continuity. All three notions are defined by using the concept of a locally closed set. A subset S of a topological space X is locally closed if it is the intersection of an open and a closed set. We discuss some properties of these functions and show that a function between topological spaces is continuous if and only if it is sub‐LC‐continuous and nearly continuous in the sense of Ptak. Several examples are provided to illustrate the behavior of these new classes of functions.