International Research Journal of Pure Algebra-Vol.-4(3), March – 2014 419 International Research Journal of Pure Algebra -4(3), 2014, 419-425 Available online through www.rjpa.info ISSN 2248–9037 GENERALIZED ALPHA GENERALIZED CLOSED SETS IN BITOPOLOGICAL SPACES Qays Hatem Imran* Al-Muthanna University, College of Education, Department of Mathematics, Al-Muthanna, Iraq. (Received on: 12-02-14; Revised & Accepted on: 21-02-14) ABSTRACT In this paper, we introduce generalized alpha generalized closed sets (gg - closed sets) in bitopological spaces and basic properties of these sets are analyzed. Further we define and study gg - continuous mappings in bitopological spaces and some of their properties have been investigated. Keywords: Bitopological space , - - g g ij  closed set , - - g g ij  open set , - - g g T ij  space , - - g g ij  continuous mappings. 1. INTRODUCTION A triple ) , , ( 2 1   X , where X is a non empty set and 1  , 2  are topologies on X is called a bitopological space and J. C. Kelly [2] initiated the study of such spaces. In 1990 , M. Jelic [3] introduced the concepts of alpha open sets in bitopological spaces. In 1986 , T. Fukutake [6] introduced the concepts of generalized closed sets in bitopological spaces and after that several authors turned their attention towards generalizations of various concepts of topology by considering bitopological spaces. O. A. El-Tantawy and H. M. Abu-Donia [5] introduced alpha generalized closed sets in bitopological spaces. In 2012,V. Seenivasan and S. Kalaiselvi [7] introduced and studied the concepts of generalized semi generalized closed sets in bitopological spaces. The purpose of this paper is to introduce a new class of closed sets called generalized alpha generalized closed sets (gg - closed sets) and generalized alpha generalized continuous mappings (gg - continuous mappings) in bitopological spaces and investigate some of their properties. 2. PRELIMINARIES Throughout this paper X , Y and Z always represent non empty bitopological spaces ) , , ( 2 1   X , ) , , ( 2 1   Y and ) , , ( 2 1   Z on which no separation axioms are assumed unless explicitly mentioned and the integers } 2 , 1 { , ,  k j i . For a subset A of X ) ( - A cl i  ( resp. ) ( int - A i  , ) ( - A cl i   ) denote the closure ( resp. interior ,  - closure ) of A with respect to the topology i  . By ) , ( j i we mean the pair of topologies ) , ( j i   . Definition: 2.1 A subset A of a bitopological space ) , , ( 2 1   X is called (i) - -  ij open [3] if ))) int( - ( - int( - A cl A i j i     , where 2 , 1 , ;   j i j i . (ii) - -  ij closed [3] if A X  is - -  ij open, where 2 , 1 , ;   j i j i . Equivalently, a subset A of a bitopological space ) , , ( 2 1   X is called - -  ij closed if A A cl cl j i j  ))) ( - ( int - ( -    . *Corresponding author: Qays Hatem Imran* Al-Muthanna University, College of Education, Department of Mathematics, Al-Muthanna, Iraq. E-mail: alrubaye84@yahoo.com