ISSN: 2320-5407 Int. J. Adv. Res. 5(7), 2722-2730 2722 Journal Homepage: - www.journalijar.com Article DOI:10.21474/IJAR01/5016 DOI URL: http://dx.doi.org/10.21474/IJAR01/5016 RESEARCH ARTICLE g # b -CLOSED SETS IN TOPOLOGICAL SPACES. S. Chandrasekar 1 , A. Atkinswestley 2 and M. Sathyabama 3 . 1.Department of Mathematics, Arignar Anna Government Arts college,Namakkal(DT)Tamil Nadu, India. 2.Department of Mathematics, Roever College of Engineering and Technology , Perambalur(DT). 3. Department of Mathematics,Periyar University Constituent College of Arts&Science,Idappadi,Salem. ………………………………………………………………………………………………….... Manuscript Info Abstract ……………………. ……………………………………………………………… Manuscript History Received: 28 May 2017 Final Accepted: 30 June 2017 Published: July 2017 Key words:- g # b -closed sets,g # b -open sets,g # b- Neighbourhoods and g # b -Limit points In topological spaces closed sets and open sets are highly used in many practical and engineering problems.In this paper a new class of sets, namely g # b -closed sets is introduced in topological spaces. Moreover we analyze the relations between g # b -closed sets and already existing various closed sets. Also we find some basic properties and applications of g # b-closed, g # b-Neighbourhoods and g # b -Limit points Copy Right, IJAR, 2017,. All rights reserved. …………………………………………………………………………………………………….... Introduction:- Generalized closed sets play a very important role in general topology and they are now the research topics of many topologists worldwide. Generalized closed sets have been studied extensively in recent years by many topologists. The investigation of generalized closed sets has led to several new and interesting results,In1963, N.Levine [5] introduced semi-open sets in topology and studied their properties. N.Levine [6] introduced the concept of generalized closed sets and studied their properties in 1970. Mashhour [9] [1982] introduced pre-open sets in topological spaces. Andrijevic [1] introduced one such new version called b-open sets in 1996.Maki, et al.[1993] [8] introduced generalized - closed and -generalized closed sets (briefly, g-closed, g-closed). M. K. R. S. VeeraKumar [18](2003), g # -closed sets in topological spaces. In this paper, we introduce a new class of generalized closed sets called g # b-closed sets in topological spaces and its various properties are discussed Preliminaries:- Throughout this paper (X, ) (or simply X) represent topological spaces ,For a subset A of X, cl(A), int(A) and A c denote the closure of A, the interior of A and the complement of A respectively. Let us recall the following definition, which are useful in the sequel. Definition 2.1 A subset A of a space (X, ) is called a (i). Pre open set[9] if A int(cl(A)). (ii). semi-open set[5] if A  cl(int(A)) . (iii). -open set [8] if A int(cl(int(A))). (iv). b-open [1] if A  cl(int(A))ڂint(cl(A)), (v). *b-open [10] if A  cl (int (A)) ځint (cl (A)). (v). b # -open [15] if A = cl(int(A))ڂint(cl(A)), Corresponding Author:-S. Chandrasekar. Address:-Assistant Professor, Department of Mathematics, Arignar Anna Government Arts college,Namakkal(DT),Tamil Nadu, India.