COMPLETENESS IN FUZZY UNIFORM SPACES

Abstract

The notion of a complete fuzzy set in a fuzzy uniform space is defined in terms of the previously defined notion of a Cauchy prefilter. Various characterisation theorems are obtained and it is shown that this is a good extension of the notion of a complete subset of a uniform space. The theory of complete fuzzy sets in a fuzzy uniform space is developed and this theory generalises the theory of complete subsets of a uniform space.