Abstract
Haver's property C turns out to be related to Borst's transfinite extension of the covering dimension. We prove that, for a uncountably many countable ordinals β there exists a strongly universal kω-space for the class of spaces of transfinite covering dimension <β. In some sense, our result is a kω-counterpart of Radul's theorem on existence of absorbing sets of given transfinite covering dimension.
Publisher
Odessa National Academy of Food Technologies
Subject
Applied Mathematics,Geometry and Topology,Analysis
Reference23 articles.
1. [1] David F. Addis, John H. Gresham. A class of infinite-dimensional spaces. I. Dimension theory and Alexandroff's problem. Fund. Math., 101(3):195-205, 1978,
2. doi: 10.4064/fm-101-3-195-205.
3. [2] Taras Banakh, Olena Hryniv. Free topological inverse semigroups as infinitedimensional manifolds. pages 132-139, 2002.
4. [3] Taras Banakh, Dušan Repovš. On linear realizations and local self-similarity of the universal Zarichnyĭ map. Houston J. Math., 31(4):1103-1114, 2005.
5. [4] Taras Banakh, Katsuro Sakai. Characterizations of (R8, σ)- or (Q8, Σ)-manifolds and their applications. Topology Appl., 106(2):115-134, 2000,