Int. Journal of Math. Analysis, Vol. 5, 2011, no. 24, 1175 - 1184 Generalized Closed Sets in Bigeneralized Topological Spaces Wichai Dungthaisong, Chawalit Boonpok and Chokchai Viriyapong Department of Mathematics, Faculty of Science Mahasarakham University, Mahasarakham 44150, Thailand lion chai@hotmail.com, chawalit boonpok@hotmail.com Abstract The purpose of the present paper is to introduce the concept of μ (m,n) -closed sets in bigeneralized topological spaces and study some of their properties. We introduce the notion of g (m,n) -continuous func- tions on bigeneralized topological spaces and investigate some of their characterizations. Mathematics Subject Classification: 54A05, 54A10 Keywords: generalized topological space, bigeneralized topological space, μ (m,n) -closed set, g (m,n) - continuous function 1 Introduction Generalized closed sets in a topological space were introduced by Levin [9] in order to extend many of the important properties of closed sets to a larger family. For instance, it was shown that compactness, normality and com- pleteness in a uniform space are inherited by generalized closed subsets. The study of bitopological spaces was first initiated by Kelly [8] and thereafter a large number of papers have been done to generalize the topological concepts to bitopological setting. Fukutake [7] introduced generalized closed sets and pairwise generalized closure operator in bitopological spaces. He defined a set A of a bitopological space X to be τ i τ j -generalized closed sets if τ j -Cl(A) ⊆ U whenever A ⊆ U and U is τ i -open in X . Also, he defined a new closure oper- ator and strongly pairwise T 1 2 -space. ´ A. Cs´ asz´ ar [3] introduced the concepts of generalized neighborhood systems and generalized topological spaces. He also introduced the concepts of continuous functions and associated interior and closure operators on generalized neighborhood systems and generalized