# Moscow spaces, Pestov-Tkačenko Problem, and $C$-embeddings

Commentationes Mathematicae Universitatis Carolinae (2000)

- Volume: 41, Issue: 3, page 585-595
- ISSN: 0010-2628

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topArhangel'skii, Aleksander V.. "Moscow spaces, Pestov-Tkačenko Problem, and $C$-embeddings." Commentationes Mathematicae Universitatis Carolinae 41.3 (2000): 585-595. <http://eudml.org/doc/248634>.

@article{Arhangelskii2000,

abstract = {We show that there exists an Abelian topological group $G$ such that the operations in $G$ cannot be extended to the Dieudonné completion $\mu G$ of the space $G$ in such a way that $G$ becomes a topological subgroup of the topological group $\mu G$. This provides a complete answer to a question of V.G. Pestov and M.G. Tkačenko, dating back to 1985. We also identify new large classes of topological groups for which such an extension is possible. The technique developed also allows to find many new solutions to the equation $\upsilon X\times \upsilon Y=\upsilon (X\times Y)$. The key role in the approach belongs to the notion of Moscow space which turns out to be very useful in the theory of $C$-embeddings and interacts especially well with homogeneity.},

author = {Arhangel'skii, Aleksander V.},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {Moscow space; Dieudonné completion; Hewitt-Nachbin completion; $C$-embedding; $G_\delta $-dense set; topological group; Souslin number; tightness; canonical open set; Dieudonné completion; Rajkov completion; Hewitt-Nachbin completion; -embedding; topological group},

language = {eng},

number = {3},

pages = {585-595},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Moscow spaces, Pestov-Tkačenko Problem, and $C$-embeddings},

url = {http://eudml.org/doc/248634},

volume = {41},

year = {2000},

}

TY - JOUR

AU - Arhangel'skii, Aleksander V.

TI - Moscow spaces, Pestov-Tkačenko Problem, and $C$-embeddings

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2000

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 41

IS - 3

SP - 585

EP - 595

AB - We show that there exists an Abelian topological group $G$ such that the operations in $G$ cannot be extended to the Dieudonné completion $\mu G$ of the space $G$ in such a way that $G$ becomes a topological subgroup of the topological group $\mu G$. This provides a complete answer to a question of V.G. Pestov and M.G. Tkačenko, dating back to 1985. We also identify new large classes of topological groups for which such an extension is possible. The technique developed also allows to find many new solutions to the equation $\upsilon X\times \upsilon Y=\upsilon (X\times Y)$. The key role in the approach belongs to the notion of Moscow space which turns out to be very useful in the theory of $C$-embeddings and interacts especially well with homogeneity.

LA - eng

KW - Moscow space; Dieudonné completion; Hewitt-Nachbin completion; $C$-embedding; $G_\delta $-dense set; topological group; Souslin number; tightness; canonical open set; Dieudonné completion; Rajkov completion; Hewitt-Nachbin completion; -embedding; topological group

UR - http://eudml.org/doc/248634

ER -

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