Geodesic
Extensions of topological and semitopological groups and the product operation
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 1, pp. 173-186 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

The main results concern commutativity of Hewitt-Nachbin realcompactification or Dieudonné completion with products of topological groups. It is shown that for every topological group $G$ that is not Dieudonné complete one can find a Dieudonné complete group $H$ such that the Dieudonné completion of $G\times H$ is not a topological group containing $G\times H$ as a subgroup. Using Korovin's construction of $G_\delta$-dense orbits, we present some examples showing that some results on topological groups are not valid for semitopological groups.
The main results concern commutativity of Hewitt-Nachbin realcompactification or Dieudonné completion with products of topological groups. It is shown that for every topological group $G$ that is not Dieudonné complete one can find a Dieudonné complete group $H$ such that the Dieudonné completion of $G\times H$ is not a topological group containing $G\times H$ as a subgroup. Using Korovin's construction of $G_\delta$-dense orbits, we present some examples showing that some results on topological groups are not valid for semitopological groups.
Classification : 22A05, 54B10, 54D35, 54D60, 54H11
Keywords: topological group; Dieudonné completion; PT-group; realcompactness; \newline Moscow space; $C$-embedding; product 
@article{CMUC_2001_42_1_a12,
     author = {Arhangel'skii, A. V. and Hu\v{s}ek, M.},
     title = {Extensions of topological and semitopological groups and the product operation},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {173--186},
     year = {2001},
     volume = {42},
     number = {1},
     mrnumber = {1825381},
     zbl = {1053.54043},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2001_42_1_a12/}
}
TY  - JOUR
AU  - Arhangel'skii, A. V.
AU  - Hušek, M.
TI  - Extensions of topological and semitopological groups and the product operation
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2001
SP  - 173
EP  - 186
VL  - 42
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/CMUC_2001_42_1_a12/
LA  - en
ID  - CMUC_2001_42_1_a12
ER  - 
%0 Journal Article
%A Arhangel'skii, A. V.
%A Hušek, M.
%T Extensions of topological and semitopological groups and the product operation
%J Commentationes Mathematicae Universitatis Carolinae
%D 2001
%P 173-186
%V 42
%N 1
%U http://geodesic.mathdoc.fr/item/CMUC_2001_42_1_a12/
%G en
%F CMUC_2001_42_1_a12
Arhangel'skii, A. V.; Hušek, M. Extensions of topological and semitopological groups and the product operation. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 1, pp. 173-186. http://geodesic.mathdoc.fr/item/CMUC_2001_42_1_a12/