Two types of remainders of topological groups
Commentationes Mathematicae Universitatis Carolinae (2008)
- Volume: 49, Issue: 1, page 119-126
- ISSN: 0010-2628
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topArhangel'skii, Aleksander V.. "Two types of remainders of topological groups." Commentationes Mathematicae Universitatis Carolinae 49.1 (2008): 119-126. <http://eudml.org/doc/250448>.
@article{Arhangelskii2008,
abstract = {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, 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.},
author = {Arhangel'skii, Aleksander V.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {remainder; compactification; topological group; $p$-space; Lindelöf $p$-space; metrizability; countable type; Lindelöf space; pseudocompact space; $\pi $-base; compactification; remainder; compactification; topological group; -space},
language = {eng},
number = {1},
pages = {119-126},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Two types of remainders of topological groups},
url = {http://eudml.org/doc/250448},
volume = {49},
year = {2008},
}
TY - JOUR
AU - Arhangel'skii, Aleksander V.
TI - Two types of remainders of topological groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2008
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 49
IS - 1
SP - 119
EP - 126
AB - 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, 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.
LA - eng
KW - remainder; compactification; topological group; $p$-space; Lindelöf $p$-space; metrizability; countable type; Lindelöf space; pseudocompact space; $\pi $-base; compactification; remainder; compactification; topological group; -space
UR - http://eudml.org/doc/250448
ER -
References
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Citations in EuDML Documents
top- Aleksander V. Arhangel'skii, The Baire property in remainders of topological groups and other results
- Aleksander V. Arhangel'skii, J. van Mill, Nonnormality of remainders of some topological groups
- Aleksander V. Arhangel'skii, Miroslav Hušek, Closed embeddings into complements of -products
- Liang-Xue Peng, Yu-Feng He, A note on topological groups and their remainders
- D. Basile, Angelo Bella, About remainders in compactifications of homogeneous spaces
- Aleksander V. Arhangel'skii, A generalization of Čech-complete spaces and Lindelöf -spaces
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