DISCRETE UNIFORM STRUCTURES AND QUASITOPOI

Abstract

It is known that no non-trivial subcategory of the category of topological spares is a quasitopos in the sense of Penon. The purpose of this note is to establish the existence of a proper class of sub-categories of the category of uniform spaces which are quasitopoi. These subcategories are generated by certain proximally discrete uniform spaces which correspond to each infinite regular cardinal.