On Ro and R1 Properties in Fuzzy Topological Spaces

Abstract

The goal of this thesis is to find out some new R1 -concepts for fuzzy topological spaces. Besides some concepts of fuzzy R0, R1, T0, T1, T2 and regular topological spaces that are already existing in the literature are recalled. In this work, twelve R1 -axioms of fuzzy R1 -topological spaces are introduced and studied in detail. Interrelations among various R1 concepts of fuzzy topological spaces are discussed. In analogy with the well-known topological properties, a complete answer is given with regard to all possible (R1 ^ T0 = T2) and (R1 ⇒ R0)-type implications for fuzzy topological spaces. It is also shown that, though a regular topological space is also a R1 -topological space, this is not true for fuzzy topological spaces.