Open AccessInfinite-dimensional manifolds related to C-spaces
Author(s) -
Mykhailo Zarichnyi,
Oryslava Polivoda
Publication year - 2020
Publication title -
trudy meždunarodnogo geometričeskogo centra/pracì mìžnarodnogo geometričnogo centru
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.124
H-Index - 2
eISSN - 2409-8906
pISSN - 2072-9812
DOI - 10.15673/tmgc.v13i3.1856
Subject(s) - transfinite number , mathematics , countable set , dimension (graph theory) , pure mathematics , extension (predicate logic) , space (punctuation) , class (philosophy) , discrete mathematics , computer science , artificial intelligence , programming language , operating system
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.