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Title: Two types of remainders of topological groups (English)
Author: Arhangel'skii, A. V.
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 49
Issue: 1
Year: 2008
Pages: 119-126
Category: math
Summary: We prove a Dichotomy Theorem: for each Hausdorff compactification $bG$ of an arbitrary topological group $G$, the remainder $bG\setminus G$ is either pseudocompact or Lindelöf. It follows that if a remainder of a topological group is paracompact or Dieudonne complete, then the remainder is Lindelöf, and the group is a paracompact $p$-space. This answers a question in A.V. Arhangel'skii, {\it Some connections between properties of topological groups and of their remainders\/}, Moscow Univ. Math. Bull. 54:3 (1999), 1--6. It is shown that every Tychonoff space can be embedded as a closed subspace in a pseudocompact remainder of some topological group. We also establish some other results and present some examples and questions. (English)
Keyword: remainder
Keyword: compactification
Keyword: topological group
Keyword: $p$-space
Keyword: Lindelöf $p$-space
Keyword: metrizability
Keyword: countable type
Keyword: Lindelöf space
Keyword: pseudocompact space
Keyword: $\pi $-base
Keyword: compactification
MSC: 54A25
MSC: 54B05
idZBL: Zbl 1212.54086
idMR: MR2433629
Date available: 2009-05-05T17:06:53Z
Last updated: 2013-09-22
Stable URL:
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Reference: [3] Arhangel'skii A.V.: Some connections between properties of topological groups and of their remainders.Moscow Univ. Math. Bull. 54:3 (1999), 1-6. MR 1711899
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