Decomposition of Generalized Closed Sets in Supra Topological Spaces

Abstract

ABSTRACT In this paper, we introduce a new class of sets called supra generalized locally closed sets and new class of maps called supra generalized locally continuous functions. Furthermore, we obtain some of their properties. KEYWORDS S-GLC sets, S-GLC* sets, S-GLC** sets, S-GL- continuous, S-GL*- continuous, S-GL**- continuous, S-GL- Let A be a subset (X, µ). irresolute, S-GL*- irresolute and S-GL**- irresolute 1. INTRODUCTION In 1921, Kuratowski and Sierpinski [8] considered the difference of two closed subsets of an n-dimensional Euclidean space. Implicit in their work is the notion of a locally closed subset of a topological space. Bourbaki [2] defined a subset of space (X, τ) is called locally closed, if it is the intersection of an open set and a closed set. 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 LC-continuous 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. In 2008, Devi et al. [3] introduced and studied a class of sets and maps between topological spaces called supra –open sets and supra –continuous maps, respectively. In 2010, O.R. Sayed et al.[12], introduced and studied a class of sets and a class of maps between topological spaces called supra b–open sets and supra b–continuous maps, respectively. Supra g-closed sets, supra g-continous function and supra g-closed maps are introduced and investigated by Ravi et al. [10]. In this paper we introduce the concept of supra generalized locally closed sets and study its basic properties. Also we introduce the concepts of supra generalized locally continuous functions and investigate some of the basic properties for this class of functions. implies s