Locally closed sets and LC‐continuous functions

Abstract

ABSTPCT. 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

G#P#-Closed Sets in a Topological Spaces

“…Proof. Ganster and Reilly [7] proved that (X,τ) is submaximal iff every subset of X is locally closed.…”

Another Decomposition of Continuity

“…Recently, we [8] defined the notion of LC-continuity, and showed that it is a continuity dual of near continuity. This decomposition of continuity has been generalized [7].…”

Decomposition of Generalized Closed Sets in Supra Topological Spaces

“…Stone [11] has used the term FG for a locally closed subset. Ganster and Reilly [4] and [5], Balachandran et al [1] and J. H. Park et al [6] introduced the concept of LCcontinuous functions, GLC continuous functions and SGLC*-continuous functions respectively. Mashhour et al [9] introduced the supra topological spaces and studied S-continuous functions and S*-continuous functions.…”