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
Totally non-remote points in
Totally nonremote points in are constructed. The number of these points is .
Totally proper forcing and the Moore-Mrówka problem
We describe a totally proper notion of forcing that can be used to shoot uncountable free sequences through certain countably compact non-compact spaces. This is almost (but not quite!) enough to produce a model of ZFC + CH in which countably tight compact spaces are sequential-we still do not know if the notion of forcing described in the paper can be iterated without adding reals.
Transfinite cardinal dimension and separability
Transfinite metrics, sequences and topological properties
Trennung und Zusammenhang.
True preimages of compact or separable sets for functional analysts
We discuss various results on the existence of ‘true’ preimages under continuous open maps between -spaces, -lattices and some other spaces. The aim of the paper is to provide accessible proofs of this sort of results for functional-analysts.
T-sequential topological spaces
Two cardinal inequalities for functionally Hausdorff spaces
In this paper, two cardinal inequalities for functionally Hausdorff spaces are established. A bound on the cardinality of the -closed hull of a subset of a functionally Hausdorff space is given. Moreover, the following theorem is proved: if is a functionally Hausdorff space, then .
Two classes of locally compact sober spaces.
Two countable, biconnected, not widely connected Hausdorff spaces.
Two countable Hausdorff almost regular spaces every continuous map of which into every Urysohn space is constant.
Two examples of pseudo-radial spaces
Two Examples of Q-topologies
Two examples of Q-topologies.
Two improvements on Tkačenko's addition theorem
We prove that (A) if a countably compact space is the union of countably many subspaces then it is compact; (B) if a compact space is the union of fewer than = left-separated subspaces then it is scattered. Both (A) and (B) improve results of Tkačenko from 1979; (A) also answers a question that was raised by Arhangel’skiǐ and improves a result of Gruenhage.