IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 14, Issue 4 Ver. I (Jul - Aug 2018), PP 43-47 www.iosrjournals.org DOI: 10.9790/5728-1404014347 www.iosrjournals.org 43 | Page On Decomposition of g * Closed Sets in Topological Spaces C.Dhanapakyam, K.Indirani Department of Mathematics Rathnavel subramaniam College of Arts & Science Coimbatore-, India Nirmala College for women Red fields,Coimbatore-,India Corresponding Author: C.Dhanapakyam Abstract: The aim of this paper is to introduced and study the classes of g * -locally closed set and different notions of generalization of continuous functions namely  g * lc-continuity,  g * lc*-continuity and  g * lc**- continuity and their corresponding irresoluteness were studied.. Keywords: g * -separated, g * -dense, g * -submaximal, g * lc-continuity, g * lc*-continuity g * lc**-continuity. --------------------------------------------------------------------------------------------------------------------------------------- Date of Submission: 02-07-2018 Date of acceptance: 18-07-2018 --------------------------------------------------------------------------------------------------------------------------------------- I. Introduction: The first step of locally closedness was done by Bourbaki [2]. He defined a set A to be locally closed if it is the intersection of an open and a closed set. In literature many general topologists introduced the studies of locally closed sets. Extensive research on locally closedness and generalizing locally closedness were done in recent years. Stone [7] used the term LC for a locally closed set. Ganster and Reilly used locally closed sets in [4] to define LC-continuity and LC-irresoluteness. Balachandran et al [1] introduced the concept of generalized locally closed sets. The aim of this paper is to introduce and study the classes of g * locally closed set and different notions of generalization of continuous functions namely  g * lc-continuity,  g * lc*-continuity and g * lc**-continuity and their corresponding irresoluteness were studied. II. Preliminary Notes Throughout this paper (X,IJ), (Y,ı) are topological spaces with no separation axioms as sumed unless otherwise stated. Let AX. The closure of A and the interior of A will be denoted by Cl(A) and Int(A) respectively. Definition 2.1. A Subset S of a space (X,IJ) is called (i) locally closed (briefly lc )[6] if S=UתF, where U is open and F is closed in (X,IJ). (ii) r-locally closed (briefly rlc ) if S=UתF, where U is r-open and F is r-closed in (X,IJ). (iii) generalized locally closed (briefly glc ) [1] if S=UתF, where U is g-open and F is g-closed in (X,IJ). Definition 2.2. [4] A subset A of a topological space (X,IJ) is called g * -closed if gcl(A)⊆U whenever A⊆U and U is -open subset of X. Definition 2.3. For a subset A of a space X, g * -cl(A) = ⋂{F: A⊆F, F is g * closed in X} is called the g * - closure of A. Remark 2.4. For a topological space (X,IJ), the following statements hold: (1) Every closed set is g * -closed but not conversely [4]. (2) Every g-closed set is g * -closed but not conversely [4]. (3) Every g*-closed set is g * -closed but not conversely [4]. (4) A subset A of X is g * -colsed if and only if g * -cl(A)=A. (5) A subset A of X is g * -open if and only if g * -int(A)=A. Corollary 2.5. If A is a g * -closed set and F is a closed set, then A∩F is a g * -closed set. Definition 2.6[5]: A function f:(X, ) →(Y,) is called g* continuous if f -1 (V) is g* closed subset of (X,) for every closed subset V of (Y,). Definition 2.7. A function f:(X,IJ)→(Y,ı) is called i) LC-continuous [6] if f -1 (V)∈ LC(X,IJ) for every V∈ı. ii) GLC-continuous [1] if f -1 (V)∈ GLC(X,IJ) for every V∈ı. Definition 2.8. A subset S of a space (X,IJ) is called (i) submaximal [3] if every dense subset is open. (ii) g-submaximal [1] if every dense subset is g-open.