$m$-bounded uniformities between two given uniformities

Totally bounded frame quasi-uniformities

This paper considers totally bounded quasi-uniformities and quasi-proximities for frames and shows that for a given quasi-proximity ⊳ on a frame L there is a totally bounded quasi-uniformity on L that is the coarsest quasi-uniformity, and the only totally bounded quasi-uniformity, that determines ⊳. The constructions due to B. Banaschewski and A. Pultr of the Cauchy spectrum ψL and the compacti...

Contextual Uniformities

Commutator Theory for Uniformities

We investigate commutator operations on compatible uniformities. We present a commutator operation for uniformities in the congruence-modular case which extends the commutator on congruences, and explore its properties. Introduction The purpose of this paper is to generalize the commutator of congruences to a commutator of compatible uniformities. Commutator theory (on congruences) works best f...

Functional Uniformities

This result suggests that every uniformity on X can be defined by means of a family of sets of real bounded continuous functions, and that important uniformities on X (such as precompact [l ] ones) are definable by means of "nice" sets of such functions. These and related problems are investigated here. A family J of sets of real functions will be said to separate a topological space X if for e...

Uniformities on Free Semigroups

Résumé. On sait que les complétions profinies d’un semigroupe libre qui sont associées à une pseudovariété de semigroupes ou de semigroupes ordonnés peuvent être définies par un écart ou un quasi-écart. Nous caractérisons les quasi-écarts et les quasi-uniformités qui peuvent être obtenues de cette façon. Nous démontrons également l’existence d’une correspondance injective “à la Eilenberg”, entr...