We demonstrate a one-to-one correspondence between idempotent closure operators and the so-called saturated quasi-uniform structures on category C. Not only this result allows to obtain categorical counterpart P of Császár-Pervin quasi-uniformity P, that we characterize as transitive compatible with an interior operator, but also permits describe those topogenous orders are induced by The P⁎ P−...

It is shown that some familiar properties of epimorphisms in the category of frames cary over to the category of uniform frames. This is achieved by suitably enriching certain frame homomorphisms to uniform frame homomorphisms. This note deals with the natural question, apparently never considered so far, whether certain familiar facts concerning epimorphisms, and specifically epi-extensions, o...