On a theorem of W.W. Comfort and K.A. Ross

Aleksander V. Arhangel'skii

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 1, page 133-151
  • ISSN: 0010-2628

Abstract

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A well known theorem of W.W. Comfort and K.A. Ross, stating that every pseudocompact group is C -embedded in its Weil completion [5] (which is a compact group), is extended to some new classes of topological groups, and the proofs are very transparent, short and elementary (the key role in the proofs belongs to Lemmas 1.1 and 4.1). In particular, we introduce a new notion of canonical uniform tightness of a topological group G and prove that every G δ -dense subspace Y of a topological group G , such that the canonical uniform tightness of G is countable, is C -embedded in G .

How to cite

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Arhangel'skii, Aleksander V.. "On a theorem of W.W. Comfort and K.A. Ross." Commentationes Mathematicae Universitatis Carolinae 40.1 (1999): 133-151. <http://eudml.org/doc/248387>.

@article{Arhangelskii1999,
abstract = {A well known theorem of W.W. Comfort and K.A. Ross, stating that every pseudocompact group is $C$-embedded in its Weil completion [5] (which is a compact group), is extended to some new classes of topological groups, and the proofs are very transparent, short and elementary (the key role in the proofs belongs to Lemmas 1.1 and 4.1). In particular, we introduce a new notion of canonical uniform tightness of a topological group $G$ and prove that every $G_\delta $-dense subspace $Y$ of a topological group $G$, such that the canonical uniform tightness of $G$ is countable, is $C$-embedded in $G$.},
author = {Arhangel'skii, Aleksander V.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {topological group; pseudocompact; Frechet-Urysohn; $G_\delta $-dense; $C$-embedded; Moscow space; canonical uniform tightness; Hewitt completion; Rajkov completion; bounded set; extremally disconnected; normal space; $k_1$-space; topological group; pseudocompact space; C-embedding; extremally disconnected space},
language = {eng},
number = {1},
pages = {133-151},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On a theorem of W.W. Comfort and K.A. Ross},
url = {http://eudml.org/doc/248387},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Arhangel'skii, Aleksander V.
TI - On a theorem of W.W. Comfort and K.A. Ross
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 1
SP - 133
EP - 151
AB - A well known theorem of W.W. Comfort and K.A. Ross, stating that every pseudocompact group is $C$-embedded in its Weil completion [5] (which is a compact group), is extended to some new classes of topological groups, and the proofs are very transparent, short and elementary (the key role in the proofs belongs to Lemmas 1.1 and 4.1). In particular, we introduce a new notion of canonical uniform tightness of a topological group $G$ and prove that every $G_\delta $-dense subspace $Y$ of a topological group $G$, such that the canonical uniform tightness of $G$ is countable, is $C$-embedded in $G$.
LA - eng
KW - topological group; pseudocompact; Frechet-Urysohn; $G_\delta $-dense; $C$-embedded; Moscow space; canonical uniform tightness; Hewitt completion; Rajkov completion; bounded set; extremally disconnected; normal space; $k_1$-space; topological group; pseudocompact space; C-embedding; extremally disconnected space
UR - http://eudml.org/doc/248387
ER -

References

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