Quasi-uniform structures determined by closure operators

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−1 is characterized operator. When applied other categories outside topology allows, among things, generate family Grp, groups group homomorphisms, determined normal closure.