Fuzzy uniform convergence and equicontinuity

Abstract

In our earlier papers we investigated function space structures in FTS, the category of fuzzy topological spaces and in FCS, the category of fuzzy convergence spaces. This paper is devoted to the study of function space structures in FUS, the category of fuzzy uniform spaces due to Lowen. We develop the basic theory and give examples of such structures such as pointwise and compact convergence. We consider separation axioms in these fuzzy function spaces and show that the fuzzy uniformity of uniform convergence is conjoining for C( X, Y). We define a notion of equicontinuous sets of mappings on which pointwise and compact convergence coincide.