Some Properties of Partial Fuzzy Metric Topology

Abstract

The objective of this work is to study some topological properties of partial fuzzy metric spaces. For this purpose, we first define a topology generated by the partial fuzzy metric in the sense of Sedghi et al. [8] We give some relationships between the topologies induced by partial metric and partial fuzzy metric. Then, we investigate various properties including countability, completeness and separation axioms and we give Baire’s theorem for partial fuzzy metric spaces. Finally, we obtain that partial fuzzy metric topological spaces are metrizable under some assumptions.