Topological modification of a fuzzy closure space

Abstract

Fuzzy topological spaces do not constitute a natural boundary for the validity of theorems, and many results can be extended to what are called fuzzy closure spaces. Fuzzy closure spaces have been introduced in [6], as a generalization of closure spaces [1]. In the present paper we introduce the concept of topological modification of a fuzzy closure operator. We prove that the topological modification of a fuzzy closure operator u on X is the finest topological fuzzy closure operator on X coarser than u. The interaction between the concepts of a subspace and the topological modification of a fuzzy closure operator is also examined.