Total and absolute paracompactness
Transfinite metrics, sequences and topological properties
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-theory.
Two closed categories of filters
Two examples of non-separable metrizable spaces
Two non-homeomorphic countable spaces having homeomorphic squares
Two-valued functions, non-archimedean quasi-metrics and ultraquasi-gauges
Tychonoff products of super second countable and super separable metric spaces
Über Distanzfunktionen mit Werten in angeordneten Halbgruppen.
Über metrische Räume und
Ultrametric spaces bi-Lipschitz embeddable in
It is proved that if an ultrametric space can be bi-Lipschitz embedded in , then its Assouad dimension is less than n. Together with a result of Luukkainen and Movahedi-Lankarani, where the converse was shown, this gives a characterization in terms of Assouad dimension of the ultrametric spaces which are bi-Lipschitz embeddable in .
Ultraparacompactness in certain Pixley-Roy hyperspaces
Un critère de métrisabilité d’un convexe compact à partir de
Uniform quotients of metric spaces
Uniform quotients of metrizable spaces
Uniforme Räume mit einer linear geordneten Basis.
Uniformly Convex Metric Spaces
In this paper the theory of uniformly convex metric spaces is developed. These spaces exhibit a generalized convexity of the metric from a fixed point. Using a (nearly) uniform convexity property a simple proof of reflexivity is presented and a weak topology of such spaces is analyzed. This topology, called coconvex topology, agrees with the usually weak topology in Banach spaces. An example of a CAT(0)-space with weak topology which is not Hausdorff is given. In the end existence and uniqueness...
Uniformly convex spaces, bead spaces, and equivalence conditions
The notion of a metric bead space was introduced in the preceding paper (L. Pasicki: Bead spaces and fixed point theorems, Topology Appl., vol. 156 (2009), 1811–1816) and it was proved there that every bounded set in such a space (provided the space is complete) has a unique central point. The bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces. It appears that normed bead spaces are identical with uniformly convex spaces. On the...
Universal measure zero, large Hausdorff dimension, and nearly Lipschitz maps
We prove that each analytic set in ℝⁿ contains a universally null set of the same Hausdorff dimension and that each metric space contains a universally null set of Hausdorff dimension no less than the topological dimension of the space. Similar results also hold for universally meager sets. An essential part of the construction involves an analysis of Lipschitz-like mappings of separable metric spaces onto Cantor cubes and self-similar sets.