Some Topics in Fuzzy Topological Spaces

Abstract

The concept of fuzzy set was introduced by the American Mathematician L. A. Zadeh for the first time in 1965. This provides a natural framework for generalizing many algebraic and topological concepts in various directions. Accordingly fuzzy groups, fuzzy ideals, fuzzy rings, fuzzy vector space, fuzzy measure, fuzzy topology, fuzzy topological groups, fuzzy topological vector space and many other branches have been developed all over the world during the last four decades. It is still developing in many directions. While reviewing the literature in fuzzy topology, we have seen the gap in separation axiom of fuzzy topological space, the counter part of which in ordinary topological space drew attention of several eminent mathematicians like Azad, K. K.; Chang, C. L.; Ali, D. M.; Wuyts, P.; Srivastava, A. K. and Lowen, R. etc. We aim to develop of theories of Fuzzy To, Fuzzy T1, Fuzzy T2, Fuzzy Ro, Fuzzy R1, Fuzzy Regular and Fuzzy Normal spaces analogous to its counterpart in ordinary topology. The material of the thesis has been divided into six chapters, a brief scenario of which we present as follows. Chapter one incorporates some of the basic definitions and results of fuzzy set, fuzzy topology and mappings. These results are ready references for the work in subsequent chapters. Results are stated without proof and can be seen in the papers referred to.