On fuzzy inverse systems of fuzzy topological spaces

Abstract

In this paper, we have initiated and studied the concepts of fuzzy inverse systems of fuzzy topological spaces and fuzzy continuous functions along with their fuzzy inverse limits. We have shown that every fuzzy inverse system possesses fuzzy inverse limit and fuzzy inverse limit is unique in some sense. The fuzzy inverse limit $\left(X, \psi_i\right)_I$ of a fuzzy inverse system $\left(X_i, \psi_{i j}\right)_I$ enjoys many satisfactory desired properties. Further, we have introduced a covariant functor $F \lim _{\leftarrow}$ from the category $FIS (I)$ of fuzzy inverse systems of fuzzy topological spaces and fuzzy continuous functions to the category FTS of fuzzy topological spaces and fuzzy continuous functions.