- 1 - -1 - ON FUZZY MINIMAL OPEN AND FUZZY MAXIMAL OPEN SETS IN FUZZY TOPOLOGICAL SPACES Basavaraj M. Ittanagi and 1 R. S. Wali Department of Mathematics, Siddaganga Institute of Technology, Tumkur- 572 103, Karnataka State, India E-Mail: dr.basavaraj@yahoo.co.in 1 Department of Mathematics, Bhandari and Rathi College GULEDAGUDD-587 203, Karnataka, India. E-mail: rswali@rediffmail.com Abstract: In this paper a new class of sets called fuzzy minimal open sets and fuzzy maximal open sets in fuzzy topological spaces are introduced and studied. A nonzero fuzzy open set A (1) of a fuzzy topological space X is said to be fuzzy minimal open (resp. fuzzy maximal open) set if any fuzzy open set which is contained (resp. contains) in A is either 0 or A itself (resp. either 1 or A itself). Some properties of the new concepts have been studied. 2000 Mathematics Subject Classification: 54A40. Key words and phrases: Fuzzy minimal open sets and fuzzy maximal open sets. 1. Introduction. The concept of a fuzzy subset was introduced and studied by L.A.Zadeh [4] in the year 1965. In the year 1968, C.L.Chang [1] introduced the concept of fuzzy topological space as an application of fuzzy sets to general topological spaces. 1.1 Definition: [1] A fuzzy subset A in set X is defined to be a function A: X[0, 1]. A fuzzy subset A in set X is empty iff its membership function is identically zero on X and is denoted by 0 or   . The set X can be considered Int. J. of Mathematical Sciences and Applications, Vol. 1, No. 2, May 2011 Copyright Mind Reader Publications www.ijmsa.yolasite.com