More on the fuzzy topological spaces on a fuzzy space(X, I)

The fuzzy topological space was introduced by Dip in 1999 depending on the notion of the fuzzy space (X, I). In this paper, further definitions, and theorems on fuzzy topological space (X, I), τ) fill the lack in Dip’s article. Different types of the fuzzy topology τ are investigated and illustrated such as co-finite fuzzy topology, co-countable fuzzy topology, right ray (or left ray) fuzzy topology, and standard (usual) fuzzy topology. Furthermore, boundary, exterior, dense, and isolated fuzzy point of a fuzzy subspace are presented based on the fuzzy space (X, I). Finally, fuzzy separation axioms on the fuzzy space (X, I) are introduced.