On Fuzzy Modular Spaces

Abstract

The concept of fuzzy modular space is first proposed in this paper. Afterwards, a Hausdorff topology induced by a $\beta$-homogeneous fuzzy modular is defined and some related topological properties are also examined. And then, several theorems on $\mu$-completeness of the fuzzy modular space are given. Finally, the well-known Baire’s theorem and uniform limit theorem are extended to fuzzy modular spaces.