Quasi-uniform and syntopogenous structures on categories
David Holgate, Minani Iragi · Topology and its Applications · 2019
We introduce and study an abstract notion of Császár's syntopogenous structure which provides a convenient setting to investigate a quasi-uniformity on a category. We show that a quasi-uniformity is a family of categorical closure operators. In particular, it is shown that every idempotent closure operator is quasi-uniformity. Various notions of completeness of objects and precompactness with respect to a quasi-uniformity defined in a natural way are also studied.