# Cellularity of a space of subgroups of a discrete group

Arkady G. Leiderman; Igor V. Protasov

Commentationes Mathematicae Universitatis Carolinae (2008)

- Volume: 49, Issue: 3, page 519-522
- ISSN: 0010-2628

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topLeiderman, Arkady G., and Protasov, Igor V.. "Cellularity of a space of subgroups of a discrete group." Commentationes Mathematicae Universitatis Carolinae 49.3 (2008): 519-522. <http://eudml.org/doc/250298>.

@article{Leiderman2008,

abstract = {Given a discrete group $G$, we consider the set $\mathcal \{L\}(G)$ of all subgroups of $G$ endowed with topology of pointwise convergence arising from the standard embedding of $\mathcal \{L\}(G)$ into the Cantor cube $\lbrace 0,1\rbrace ^\{G\}$. We show that the cellularity $c(\mathcal \{L\}(G))\le \aleph _0$ for every abelian group $G$, and, for every infinite cardinal $\tau $, we construct a group $G$ with $c(\mathcal \{L\}(G))=\tau $.},

author = {Leiderman, Arkady G., Protasov, Igor V.},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {space of subgroups; cellularity; Shanin number; space of subgroups; cellularity; Shanin number},

language = {eng},

number = {3},

pages = {519-522},

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

title = {Cellularity of a space of subgroups of a discrete group},

url = {http://eudml.org/doc/250298},

volume = {49},

year = {2008},

}

TY - JOUR

AU - Leiderman, Arkady G.

AU - Protasov, Igor V.

TI - Cellularity of a space of subgroups of a discrete group

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2008

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

VL - 49

IS - 3

SP - 519

EP - 522

AB - Given a discrete group $G$, we consider the set $\mathcal {L}(G)$ of all subgroups of $G$ endowed with topology of pointwise convergence arising from the standard embedding of $\mathcal {L}(G)$ into the Cantor cube $\lbrace 0,1\rbrace ^{G}$. We show that the cellularity $c(\mathcal {L}(G))\le \aleph _0$ for every abelian group $G$, and, for every infinite cardinal $\tau $, we construct a group $G$ with $c(\mathcal {L}(G))=\tau $.

LA - eng

KW - space of subgroups; cellularity; Shanin number; space of subgroups; cellularity; Shanin number

UR - http://eudml.org/doc/250298

ER -

## References

top- Engelking R., General Topology, PWN, Warszawa, 1985. Zbl0684.54001
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- Protasov I.V., 10.1007/BF01057543, Ukrain. Mat. Zh. 40 (1988), 654-658; English translation: Ukrainian Math. J. 40 (1988), 559-562. (1988) MR0971739DOI10.1007/BF01057543
- Shanin N.A., On product of topological spaces, Trudy Mat. Inst. Akad. Nauk SSSR 24 (1948), 1-112 (in Russian). (1948) MR0027310
- Tsybenko Yu.V., Dyadicity of a space of subgroups of a topological group, Ukrain. Mat. Zh. 38 (1986), 635-639. (1986) MR0870369
- Fuchs L., Infinite Abelian Groups, Vol. 1, Academic Press, New York and London, 1970. Zbl0338.20063MR0255673

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