Preliminary Concept and Result of Fuzzy Metric Space in Point Set Topology

The innovative concept of fuzzy mathematics has become one of the interesting areas of research since last fifty-five years, which was first introduced by Zadeh in 1965. Many researchers connected the fuzzy concept in different forms of metric spaces. The results about the point sets have discussed, mainly topological properties of sets, connecting with the fuzzy metric space. The propose of this paper is to study the point set topology in fuzzy metric space, especially by introducing the concept of open and closed balls and discuss some of the common properties. Moreover, we introduce the concept of compactness and pre-compactness in fuzzy metric space.