Malaya Journal of Matematik 4(1)(2013) 89–96 On  g α -sets in bitopological spaces M. Lellis Thivagar a and Nirmala Rebecca Paul b, * a School of Mathematics, Madurai Kamaraj University, Madurai–625021, Tamilnadu, India. b Department of Mathematics, Lady Doak College, Madurai–625002, Tamilnadu, India. Abstract The paper introduces  g α -closed sets in bitopological spaces and establishes the relationship between other existing sets. As an application (i, j ) g α -closure is introduced to define a new topology. We also derive a new decomposition of continuity. Keywords: τ j -open set,  g α -closed set,  g α -open set, # gs-open set. 2010 MSC: 57E05. c 2012 MJM. All rights reserved. 1 Introduction The notion of generalised closed sets introduced by Levine[7] plays a significant role in general topol- ogy. A number of generalised closed sets have been introduced and their properties are investigated. Only a few of the class of generalised closed sets form a topology. The class of  g α -closed sets[4] is one among them. Kelly[5] introduced the concepts of bitopological spaces. Many topologists have introduced different types of sets in bitopological spaces. We have introduced  g α -closed sets in bitopological spaces and discussed their basic properties. We have introduced (i, j ) g α -closure and defined a new topology. We also introduced (i, j )T  gα , (i, j ) # T  gα -spaces and derived a new decomposition of continuity in bitopological spaces. 2 Preliminaries We list some definitions which are useful in the following sections. The interior and the closure of a subset A of (X, τ ) are denoted by Int(A) and Cl(A), respectively. Throughout the paper, (X, τ 1 ,τ 2 ), (Y,σ 1 ,σ 2 ) and (Z, η 1 ,η 2 ) (or simply X, Y and Z ) represent bitopological spaces on which no separation axioms are assumed unless otherwise mentioned. For a subset A of X, A c denote the complement of A. Definition 2.1. A subset A of a topological space (X, τ ) is called (i) an ω-closed set [10] if Cl(A) ⊆ U whenever A ⊆ U and U is semi-open in (X, τ ), (ii) a *g-closed set [11] if Cl(A) ⊆ U whenever A ⊆ U and U is ω-open in (X, τ ) , (iii) a # g-semi-closed set[13](briefly # gs-closed)[12] if sCl(A) ⊆ U whenever A ⊆ U and U is *g-open in (X, τ ) and (iv)  g α closed set[4] if αCl(A) ⊆ U whenever A ⊆ U and U is # gs-open in (X, τ ) The complement of ω-closed(resp *g-closed, # gs-closed, g α -closed)set is said to be ω-open(resp *g-open, # gs- open, g α -open) * Corresponding author. E-mail addresses: mlthivagar@yahoo.co.in (M. Lellis Thivagar) and nimmi rebecca@yahoo.com (Nirmala Rebecca Paul)