More on Fuzzy Metric Type Spaces

Abstract

In this paper, we investigate the further properties of fuzzy metric type spaces introduced by Saadati [1]. We prove that a M-convergent sequence in a fuzzy metric type space has a unique limit. Later we show that for a fuzzy metric type space (X, M, *, K) if M is continuous with respect to the first (second) variable then M is continuous with respect to the second (first) variable and M-convergence are equivalent to convergence. Moreover, in such spaces open balls are open and closed balls are closed, therefore induced topology is Hausdorff, first countable, regular and metrizable.