Extensions of topological and semitopological groups and the product operation
Arhangel'skii, Aleksander V. ; Hušek, Miroslav
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001), p. 173-186 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 2001-01-01
Classification:  22A05,  54B10,  54D35,  54D60,  54H11 
@article{119232,
     author = {Aleksander V. Arhangel'skii and Miroslav Hu\v sek},
     title = {Extensions of topological and semitopological groups and the product operation},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {42},
     year = {2001},
     pages = {173-186},
     zbl = {1053.54043},
     mrnumber = {1825381},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119232}
}

Arhangel'skii, Aleksander V.; Hušek, Miroslav. Extensions of topological and semitopological groups and the product operation. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) pp. 173-186. http://gdmltest.u-ga.fr/item/119232/

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