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.
Two remarks on weaker connected topologies
It is shown that no generalized Luzin space condenses onto the unit interval and that the discrete sum of copies of the Cantor set consistently does not condense onto a connected compact space. This answers two questions from [2].
Two spaces homeomorphic to
We consider the spaces called , constructed on the set of all finite sequences of natural numbers using ultrafilters to define the topology. For such spaces, we discuss continuity, homogeneity, and rigidity. We prove that is homogeneous if and only if all the ultrafilters have the same Rudin-Keisler type. We proved that a space of Louveau, and in certain cases, a space of Sirota, are homeomorphic to (i.e., for all ). It follows that for a Ramsey ultrafilter , is a topological group....
Two theorems concerning BI-quotient maps
Two types of remainders of topological groups
We prove a Dichotomy Theorem: for each Hausdorff compactification of an arbitrary topological group , the remainder is either pseudocompact or Lindelöf. It follows that if a remainder of a topological group is paracompact or Dieudonne complete, then the remainder is Lindelöf, and the group is a paracompact -space. This answers a question in A.V. Arhangel’skii, Some connections between properties of topological groups and of their remainders, Moscow Univ. Math. Bull. 54:3 (1999), 1–6. It is...
Two-fold theorem on Fréchetness of products
A refined common generalization of known theorems (Arhangel’skii, Michael, Popov and Rančin) on the Fréchetness of products is proved. A new characterization, in terms of products, of strongly Fréchet topologies is provided.