THE FUZZY UNIFORMISATION OF FUNCTION SPACES

Abstract

It is shown that if (Y, D) is a fuzzy uniform space in the sense of Lowen and X is a set, then a fuzzy uniformity D _π, of pointwise convergence and a fuzzy uniformity D _u, of uniform convergence can be defined on Y^x . These are natural generalisations of the uniformities of pointwise and uniform convergence. The basic theory of function spaces is shown to extend to the fuzzy setting. In particular, conditions for completeness and compactness of fuzzy subsets of Y^x are established.