SUPER UNIFORM SPACES

Abstract

A new, generalized form, of uniformity, the so called super uniformity is defined and studied. It is based on the concept of fuzzy filter, as introduced by Eklund and Gaäler [EG]. To each super uniformity, a fuzzy α-uniformities system can be associated. They will be called α-levels. These α-levels are fuzzy uniformities in the sense of Lowen, for α=1, and α-modifications with pleasant properties, for α≠1. The *-version of super uniformities is related, at level 1, with T-uniformities, as defined by Höhle [Hö]. A criterion for a given family of prefilters {F ^α}_αεI0 on a set X to generate a fuzzy filter ???? on X with {F ^α)_{αε I0} as its family of α-level prefilters, that is ????_α = F ^α is found, and extended to super uniformities. Finally, super uniformities are related with fuzzy topologies in the sense of Šostak.