The decomposable and the ambiguous sets
We prove that every ambiguous subset of a hereditarily Bairespace is decomposable. We obtain that a decomposable set$Asubseteq X$ is ambiguous when (i) $X$ is a perfectlyparacompact space, or (ii) $A$ and $Xsetminus A$ are Lindel"{o}fand $X$ is a completely regular space.
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Format: | Article |
Language: | English |
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Vasyl Stefanyk Precarpathian National University
2011-12-01
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Series: | Karpatsʹkì Matematičnì Publìkacìï |
Online Access: | http://journals.pu.if.ua/index.php/cmp/article/view/98/87 |
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author | O. Karlova |
author_facet | O. Karlova |
author_sort | O. Karlova |
collection | DOAJ |
description | We prove that every ambiguous subset of a hereditarily Bairespace is decomposable. We obtain that a decomposable set$Asubseteq X$ is ambiguous when (i) $X$ is a perfectlyparacompact space, or (ii) $A$ and $Xsetminus A$ are Lindel"{o}fand $X$ is a completely regular space. |
first_indexed | 2024-12-20T04:28:36Z |
format | Article |
id | doaj.art-dd22fa0def0741a8b290f59bd710a952 |
institution | Directory Open Access Journal |
issn | 2075-9827 |
language | English |
last_indexed | 2024-12-20T04:28:36Z |
publishDate | 2011-12-01 |
publisher | Vasyl Stefanyk Precarpathian National University |
record_format | Article |
series | Karpatsʹkì Matematičnì Publìkacìï |
spelling | doaj.art-dd22fa0def0741a8b290f59bd710a9522022-12-21T19:53:27ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272011-12-01327176The decomposable and the ambiguous setsO. KarlovaWe prove that every ambiguous subset of a hereditarily Bairespace is decomposable. We obtain that a decomposable set$Asubseteq X$ is ambiguous when (i) $X$ is a perfectlyparacompact space, or (ii) $A$ and $Xsetminus A$ are Lindel"{o}fand $X$ is a completely regular space.http://journals.pu.if.ua/index.php/cmp/article/view/98/87 |
spellingShingle | O. Karlova The decomposable and the ambiguous sets Karpatsʹkì Matematičnì Publìkacìï |
title | The decomposable and the ambiguous sets |
title_full | The decomposable and the ambiguous sets |
title_fullStr | The decomposable and the ambiguous sets |
title_full_unstemmed | The decomposable and the ambiguous sets |
title_short | The decomposable and the ambiguous sets |
title_sort | decomposable and the ambiguous sets |
url | http://journals.pu.if.ua/index.php/cmp/article/view/98/87 |
work_keys_str_mv | AT okarlova thedecomposableandtheambiguoussets AT okarlova decomposableandtheambiguoussets |