The Smirnov compactification as a quotient space of the Stone-Čech compactification.
Tightness and π-character in centered spaces
We continue an investigation into centered spaces, a generalization of dyadic spaces. The presence of large Cantor cubes in centered spaces is deduced from tightness considerations. It follows that for centered spaces X, πχ(X) = t(X), and if X has uncountable tightness, then t(X) = supκ : ⊂ X. The relationships between 9 popular cardinal functions for the class of centered spaces are justified. An example is constructed which shows, unlike the dyadic and polyadic properties, that the centered...
Topologies on products and decompositions of topological spaces
Toroidal decompositions of and a family of 3-dimensional ANR’s (AR’s)
Uncountably many wild knots whose cyclic branched covering are S3.
There is a disk in S3 whose interior is PL embedded and whose boundary has a tame Cantor set of locally wild points, such that the n-fold cyclic coverings of S3 branched over the boundary of the disk are all S3. An uncountable set of inequivalent wild knots with these properties is exhibited.
Uniform quotients of metric spaces
Uniform quotients of metrizable spaces
Universal reparametrization of a family of cycles : a new approach to meromorphic equivalence relations
We study analytic families of non-compact cycles, and prove there exists an analytic space of finite dimension, which gives a universal reparametrization of such a family, under some assumptions of regularity. Then we prove an analogous statement for meromorphic families of non-compact cycles. That is a new approach to Grauert’s results about meromorphic equivalence relations.
Upper semicontinuous decompositions of convex metric spaces
Weak-bases and -spaces
It is shown that certain weak-base structures on a topological space give a -space. This solves the question by A.V. Arhangel’skii of when quotient images of metric spaces are -spaces. A related result about symmetrizable spaces also answers a question of Arhangel’skii. Theorem.Any symmetrizable space is a -space hereditarily. Hence, quotient mappings, with compact fibers, from metric spaces have a -space image. What about quotient -mappings? Arhangel’skii and Buzyakova have shown that...
О пространствах, каждое факторное отображение на которые псевдооткрыто
Универсальные элементы для семейств сепарабельных метрических пространств
Факторпространства и кратность базы