Cofinitely and co-countably projective spaces
We show that X is cofinitely projective if and only if it is a finite union of Alexandroff compactatifications of discrete spaces. We also prove that X is co-countably projective if and only if X admits no disjoint infinite family of uncountable cozero sets. It is shown that a paracompact space X is...
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Universitat Politècnica de València
2002-10-01
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doaj-3974d60a3d384ff6ad08f7651d2b90642020-11-24T21:39:48ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472002-10-013218519510.4995/agt.2002.20621669Cofinitely and co-countably projective spacesPablo Mendoza Iturralde0Vladimir V. Tkachuk1Instituto Politécnico NacionalUniversidad Autónoma MetropolitanaWe show that X is cofinitely projective if and only if it is a finite union of Alexandroff compactatifications of discrete spaces. We also prove that X is co-countably projective if and only if X admits no disjoint infinite family of uncountable cozero sets. It is shown that a paracompact space X is co-countably projective if and only if there exists a finite set B C X such that B C U ϵ τ (X) implies │X\U│ ≤ ω. In case of existence of such a B we will say that X is concentrated around B. We prove that there exists a space Y which is co-countably projective while there is no finite set B C Y around which Y is concentrated. We show that any metrizable co-countably projective space is countable. An important corollary is that every co-countably projective topological group is countable.http://polipapers.upv.es/index.php/AGT/article/view/2062Cofinitely projectiveCo-countably projectiveScattered compact |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Pablo Mendoza Iturralde Vladimir V. Tkachuk |
spellingShingle |
Pablo Mendoza Iturralde Vladimir V. Tkachuk Cofinitely and co-countably projective spaces Applied General Topology Cofinitely projective Co-countably projective Scattered compact |
author_facet |
Pablo Mendoza Iturralde Vladimir V. Tkachuk |
author_sort |
Pablo Mendoza Iturralde |
title |
Cofinitely and co-countably projective spaces |
title_short |
Cofinitely and co-countably projective spaces |
title_full |
Cofinitely and co-countably projective spaces |
title_fullStr |
Cofinitely and co-countably projective spaces |
title_full_unstemmed |
Cofinitely and co-countably projective spaces |
title_sort |
cofinitely and co-countably projective spaces |
publisher |
Universitat Politècnica de València |
series |
Applied General Topology |
issn |
1576-9402 1989-4147 |
publishDate |
2002-10-01 |
description |
We show that X is cofinitely projective if and only if it is a finite union of Alexandroff compactatifications of discrete spaces. We also prove that X is co-countably projective if and only if X admits no disjoint infinite family of uncountable cozero sets. It is shown that a paracompact space X is co-countably projective if and only if there exists a finite set B C X such that B C U ϵ τ (X) implies │X\U│ ≤ ω. In case of existence of such a B we will say that X is concentrated around B. We prove that there exists a space Y which is co-countably projective while there is no finite set B C Y around which Y is concentrated. We show that any metrizable co-countably projective space is countable. An important corollary is that every co-countably projective topological group is countable. |
topic |
Cofinitely projective Co-countably projective Scattered compact |
url |
http://polipapers.upv.es/index.php/AGT/article/view/2062 |
work_keys_str_mv |
AT pablomendozaiturralde cofinitelyandcocountablyprojectivespaces AT vladimirvtkachuk cofinitelyandcocountablyprojectivespaces |
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1725929185192443904 |