On the L-fuzzy topological spaces

As a natural generalization of fuzzy metric spaces due to George and Veeramani [George A, Veeramani P. On some result in fuzzy metric space. Fuzzy Sets Syst 1994;64:395-9], the present author defined the notion of L-fuzzy metric spaces. In this paper we prove some known results of metric spaces including Uniform continuity theorem and Ascoli-Arzela theorem for L-fuzzy metric spaces. We also prove that every L-fuzzy metric space has a countably locally finite basis and use this result to conclude that every L-fuzzy metric space is metrizable.