In this paper, the Urysohn, completely Hausdorff and completely regular axioms in $L$-topological spaces are generalized to $L$-fuzzy topological spaces. Each $L$-fuzzy topological space can be regarded to be Urysohn, completely Hausdorff and completely regular tosome degree. Some properties of them are investigated. The relations among them and $T_2$ in $L$-fuzzy topological spaces are discussed.

Gregori and Romaguera introduced, in 2004, the notion of a KM-fuzzy quasi-metric space as natural asymmetric generalization concept fuzzy metric sense Kramosil Michalek. Ever since, various authors have discussed several aspects such spaces, including their topological (quasi-)metric properties well connections with domain theory relationship other structures. In particular, development fixed p...

The main purpose of this paper is to prove the intuitionistic fuzzy contraction properties of the Hutchinson-Barnsley operator on the intuitionistic fuzzy hyperspace with respect to the Hausdorff intuitionistic fuzzy metrics. Also we discuss about the relationships between the Hausdorff intuitionistic fuzzy metrics on the intuitionistic fuzzy hyperspaces. Our theorems generalize and extend some...

We study conditions under which the Hausdorff quasi-uniformity UH of a quasi-uniform space (X,U) on the set P0(X) of the nonempty subsets of X is bicomplete. Indeed we present an explicit method to construct the bicompletion of the T0-quotient of the Hausdorff quasi-uniformity of a quasi-uniform space. It is used to find a characterization of those quasi-uniform T0spaces (X,U) for which the Hau...