On T0-and T1-fuzzy closure spaces

Abstract

In this paper, we introduce subspace of a fuzzy closure space, sum of a family of pairwise disjoint fuzzy closure spaces and product of a family of fuzzy closure spaces, for the fuzzy closure spaces denned in Srivastava et al., 1994. We also introduce the notion of a T1-fuzzy closure space. We have studied here T0-(introduced earlier in Srivastava et al., 1994) and T1-fuzzy closure spaces in detail. Several results have been proved which establish the appropriateness of the definitions. In particular, we observe that T0 and T1 satisfy the hereditary, productive and projective properties and in addition, both are "good extensions" of the corresponding concepts in a closure space. © 2000 Elsevier Science B.V. All rights reserved.