Topological semi-lattices and their underlying spaces.
A topological space is said to be generated by an ideal if for all and all there is in such that , and is said to be weakly generated by if whenever a subset of contains for every with , then itself is closed. An important class of examples are the so called weakly discretely generated spaces (which include sequential, scattered and compact Hausdorff spaces). Another paradigmatic example is the class of Alexandroff spaces which corresponds to spaces generated by finite sets....
In this paper we investigate the relations between torsion classes of Specker lattice ordered groups and torsion classes of generalized Boolean algebras.
This paper considers totally bounded quasi-uniformities and quasi-proximities for frames and shows that for a given quasi-proximity on a frame there is a totally bounded quasi-uniformity on 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 and the compactification of a uniform frame are meaningful for quasi-uniform frames. If is a totally bounded quasi-uniformity...