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.

Bibliographic Details
Main Author: O. Karlova
Format: Article
Language:English
Published: Vasyl Stefanyk Precarpathian National University 2011-12-01
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.
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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
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