www.iaset.us editor@iaset.us ON NANO (1,2)* SEMI-GENERALIZED CLOSED SETS IN NANO BITOPOLOGICAL SPACES K. BHUVANESWARI 1 & J. SHEEBA PRIYADHARSHINI 2 1 Associate Professor, Department of Mathematics, Mother Teresa Women’s University, Kodaikanal, Tamil Nadu, India. 2 Research Scholar, Department of Mathematics, Mother Teresa Women’s University, Kodaikanal, Tamil Nadu, India. ABSTRACT The purpose of this paper is to define Nano Bitopological space and study a new class of sets called Nano (1, 2)* semi-generalized closed sets in Nano Bitopological spaces. Basic properties of Nano (1, 2)* semi-generalized closed sets are analyzed. Also the new Characterization on Nano (1, 2)* semi-generalized spaces are introduced and their relation with already existing well known spaces are also investigated. KEYWORDS: Nano (1, 2)* Open Sets, Nano (1, 2)* Closed Sets, Nano (1, 2)* Closure, Nano (1, 2)* Interior, Nano (1, 2)* Semi Closed Sets, Nano (1, 2)* Semi-Closure, Nano (1, 2)* Semi-Interior, Nano (1, 2)* Semi-Generalized Closed Sets, Nano (1, 2)* Semi- 0 T , Nano (1, 2)* Semi- 1/2 T , Nano (1, 2)* Semi- 1 T 1. INTRODUCTION In 1970, Levine [11] introduced the concept of generalized closed sets as a generalization of closed sets in topological spaces. While in 1987, P.Bhattacharyya et.al. [1] Have introduced the notion of semi generalized closed sets in topological spaces. In 1975, S.N.Maheshwari et al., [12] have defined the concepts of semi separation axioms. The notion of nano topology was introduced by Lellis Thivagar [8]. In 1963, J.C.Kelly [7] initiated the study of bitopological spaces. Mean while in 1987, Fukutake [4] introduced generalized closed sets and pairwise generalized closure operator in bitopological spaces. In 1989, Fukutake [5] introduced semi open sets in bitopological spaces. In 2014, K. Bhuvaneswari et al., [3] have introduced the notion of nano semi generalized and nano generalized semi closed sets in nano topological space. In this paper, the concept of new class of sets on nano bitotpological spaces called nano (1, 2)* semi generalized closed sets and the characterization of nano (1, 2)* semi generalized spaces are introduced. Also study the relation of these new sets with the existing sets. 2. PRELIMINARIES Definition 2.1 [10]: A subset A of a topological space ( ,) X  is called a semi open set if [ ( )] A cl Int A  . The complement of a semi open set of a space X is called semi closed set in X. Definition 2.2 [1]: A semi-closure of a subset A of X is the intersection of all semi closed sets that contains A and it is denoted by scl (A). International Journal of Applied Mathematics & Statistical Sciences (IJAMSS) ISSN(P): 2319-3972; ISSN(E): 2319-3980 Vol. 5, Issue 3, Apr - May 2016; 19-30 © IASET