Abstract
Some properties of fuzzy quasimetric spaces are studied. We prove that the topology induced by any -complete fuzzy-quasi-space is a -complete quasimetric space. We also prove Baire's theorem, uniform limit theorem, and second countability result for fuzzy quasi-metric spaces.
Highlights
Introduction and PreliminariesZadeh 1 introduced the concept of fuzzy sets as a new way to represent vagueness in our everyday life
We prove that the topology induced by any M-complete fuzzy-quasi-space is a d-complete quasimetric space
Many authors regarding the theory of fuzzy sets and its applications have developed a lot of literatures
Summary
Zadeh 1 introduced the concept of fuzzy sets as a new way to represent vagueness in our everyday life. The definition proposed by Kramosil and Michalek in 1975 2 is the most accepted one which is closely related to a class of probabilistic metric spaces 6. Following this definition, a lot of research have been done on the existence of fixed points for the mappings under different conditions. Many authors have investigated and modified the definition of this concept and defined a Hausdorff topology on this fuzzy metric space. If M satisfies conditions FM1 , FM-2 , FM-3 , FM-5 , FM-6 , and FM-7 , we call M, ∗ a fuzzy metric space. Let X, M, ∗ be a fuzzy quasimetric space.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
