Infinite-dimensional manifolds related to C-spaces

Infinite-dimensional manifolds related to C-spaces

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 r...

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Main Authors: Mykhailo Zarichnyi, Oryslava Polivoda
Format: Article
Language:Russian
Published: Odessa National Academy of Food Technologies 2020-12-01
Series:Pracì Mìžnarodnogo Geometričnogo Centru
Online Access:https://journals.onaft.edu.ua/index.php/geometry/article/view/1856
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spelling doaj-d2c830f4978f498fbae169406906cc992020-12-28T07:52:03ZrusOdessa National Academy of Food TechnologiesPracì Mìžnarodnogo Geometričnogo Centru 2072-98122409-89062020-12-01133495710.15673/tmgc.v13i3.18561856Infinite-dimensional manifolds related to C-spacesMykhailo Zarichnyi0Oryslava Polivoda1Ivan Franko National University of LvivUkrainian Academy of PrintingHaver'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.https://journals.onaft.edu.ua/index.php/geometry/article/view/1856
collection DOAJ
language Russian
format Article
sources DOAJ
author Mykhailo Zarichnyi
Oryslava Polivoda
spellingShingle Mykhailo Zarichnyi
Oryslava Polivoda
Infinite-dimensional manifolds related to C-spaces
Pracì Mìžnarodnogo Geometričnogo Centru
author_facet Mykhailo Zarichnyi
Oryslava Polivoda
author_sort Mykhailo Zarichnyi
title Infinite-dimensional manifolds related to C-spaces
title_short Infinite-dimensional manifolds related to C-spaces
title_full Infinite-dimensional manifolds related to C-spaces
title_fullStr Infinite-dimensional manifolds related to C-spaces
title_full_unstemmed Infinite-dimensional manifolds related to C-spaces
title_sort infinite-dimensional manifolds related to c-spaces
publisher Odessa National Academy of Food Technologies
series Pracì Mìžnarodnogo Geometričnogo Centru
issn 2072-9812
2409-8906
publishDate 2020-12-01
description 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.
url https://journals.onaft.edu.ua/index.php/geometry/article/view/1856
work_keys_str_mv AT mykhailozarichnyi infinitedimensionalmanifoldsrelatedtocspaces
AT oryslavapolivoda infinitedimensionalmanifoldsrelatedtocspaces
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