Separation Axioms on L-Topological Spaces

Abstract

The notion of a fuzzy set, as proposed by L.A. Zadeh[90] in 1965 to provide a foundation for the evolution of many areas of knowledge. After then in quick succession, L-fuzzy sets were introduced by Goguen[24] in 1967. As a result, this provides a natural frame work for generalizing many algebraic and topological concepts in various directions such as L-fuzzy sets, fuzzy logics, fuzzy control, fuzzy groups, fuzzy rings, fuzzy vector spaces, fuzzy topology, fuzzy bitopology, L-topology etc. Many other branches of mathematics have been developed all over the world during the last five decades. Chang [12] first introduced and studied the concept of a fuzzy topological space by using the fuzzy set in 1968. Hutton[31-34] ,Reilly[33-34],Wong [83-84], Lowen[47-48], Srivastava[73-79], Dude[16-17], Cutler[14], Ying[88], Ali[2-9], Hossain[26-30], Pu and Liu[53-54], etc., discussed and developed various aspects of fuzzy topological spaces. Ying [88] introduced fuzzifying topology and developed this in a new direction with the semantic methods of continuous valued logic. With the help of fuzzifying topology, Sinha[69-70] introduced and studied T0, T1, T2-(Hausdorff), T3-(regular), T4- (normal), separation axioms. Mashhour et al. [51-52] introduced and studied the concepts of the family of fuzzifying semi-open sets, fuzzifying neighbourhood structure of a point and fuzzifying semi-closure of a fuzzy set.................