International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 3, Pages 417-424

Locally closed sets and LC-continuous functions

M. Ganster and I. L. Reilly

Department of Mathematics, University of California, Davis, California 95616, USA

Received 24 March 1988

Copyright © 1989 M. Ganster and I. L. Reilly. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.