α-COMPACTNESS OF FUZZY TOPOLOGICAL SPACES: A CATEGORICAL APPROACH

Abstract

It is shown that α-compactness (due to Gantner, Steinlage and Warren) of fuzzy topological spaces is the categorical compactness (in the sense of Herrlich, Salicrup and Strecker) which arises from a factorization structure on the category of fuzzy topological spaces and fuzzy continuous maps. Other characterizations of α-compactness are given, including characterizations in terms of fuzzy nets and fuzzy filters. The separatedness notion corresponding to the factorization structure is also identified.