We generalize a major portion of the classical theory of Cand C embedded subspaces to pointfree topology, where the corresponding notions are frame Cand C -quotients. The central results characterizeâ€¦ (More)

A frame homomorphism is coz-onto if it maps the cozero part of its domain surjectively onto that of its codomain. This captures the notion of a z-embedded subspace of a topological space in aâ€¦ (More)

We characterize monomorphisms in rLLoc, the category of regular LindelÃ¶f locales. Though somewhat complicated, the characterization is intrinsic in the sense that it refers only to the properties ofâ€¦ (More)

For n a positive integer, Ln is the variety of `-groups satisfying the equation [x, y] = e. Many of the well known but striking features of the Ln varieties carry over to varieties satisfying theâ€¦ (More)

A locallic version of Hager's metric-ne spaces is presented. A general de-nition of A-neness is given and various special cases are considered, notably A = all metric frames, A = complete metricâ€¦ (More)

A locallic version of Hagerâ€™s metric-fine spaces is presented. A general definition of A-fineness is given and various special cases are considered, notably A = all metric frames, A = complete metricâ€¦ (More)

We show that every completely regular frame has a P -frame reÂ‡ection. The proof is straightforward in the case of a LindelÃ¶f frame, but more complicated in the general case. The chief obstacle to aâ€¦ (More)

This paper presents a new description of the completion of a quasi-uniform frame. The completion is used to extend the notion of the Samuel compactification to quasi-uniform frames.