Topological properties of generalized Wallman spaces and lattice relations.
Topological properties of spaces ordered by preferences.
Topological spaces compact with respect to a set of filters
If is a family of filters over some set I, a topological space X is sequencewise -compact if for every I-indexed sequence of elements of X there is such that the sequence has an F-limit point. Countable compactness, sequential compactness, initial κ-compactness, [λ; µ]-compactness, the Menger and Rothberger properties can all be expressed in terms of sequencewise -compactness for appropriate choices of . We show that sequencewise -compactness is preserved under taking products if and only if there...
Topological spaces without -accessible diagonal
Topologically complete spaces (Summary of author's results)
Topologically maximal convergences, accessibility, and covering maps
Topologically maximal pretopologies, paratopologies and pseudotopologies are characterized in terms of various accessibility properties. Thanks to recent convergence-theoretic descriptions of miscellaneous quotient maps (in terms of topological, pretopological, paratopological and pseudotopological projections), the quotient characterizations of accessibility (in particular, those of G. T. Whyburn and F. Siwiec) are shown to be instances of a single general theorem. Convergence-theoretic characterizations...
Topologically maximal pretopologies
Topologie fine et mesure de référence.
Topologie générale et espaces d'ultrafiltres
Topologies associated to some decision statistical functions
Topologies between compact and uniform convergence on function spaces.
Topologies compatible with order and separation axioms
Topologies generated by closed intervals.
Topologies generated by ideals
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....
Topology in a category: Compactness.
Total and absolute paracompactness
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 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...
Totally Brown subsets of the Golomb space and the Kirch space
A topological space is totally Brown if for each and every nonempty open subsets of we have . Totally Brown spaces are connected. In this paper we consider the Golomb topology on the set of natural numbers, as well as the Kirch topology on . Then we examine subsets of these spaces which are totally Brown. Among other results, we characterize the arithmetic progressions which are either totally Brown or totally separated in . We also show that and are aposyndetic. Our results...
Totally disconnected compactifications.
Totally discontinuous connectivity functions