Geodesic
Cellularity of a space of subgroups of a discrete group
Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 3, pp. 519-522 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Given a discrete group $G$, we consider the set $\Cal L(G)$ of all subgroups of $G$ endowed with topology of pointwise convergence arising from the standard embedding of $\Cal L(G)$ into the Cantor cube $\{0,1\}^{G}$. We show that the cellularity $c(\Cal L(G))\leq \aleph_0$ for every abelian group $G$, and, for every infinite cardinal $\tau$, we construct a group $G$ with $c(\Cal L(G))=\tau$.
Given a discrete group $G$, we consider the set $\Cal L(G)$ of all subgroups of $G$ endowed with topology of pointwise convergence arising from the standard embedding of $\Cal L(G)$ into the Cantor cube $\{0,1\}^{G}$. We show that the cellularity $c(\Cal L(G))\leq \aleph_0$ for every abelian group $G$, and, for every infinite cardinal $\tau$, we construct a group $G$ with $c(\Cal L(G))=\tau$.
Classification : 54A25, 54B20
Keywords: space of subgroups; cellularity; Shanin number 
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     author = {Leiderman, A. and Protasov, I. V.},
     title = {Cellularity of a space of subgroups of a discrete group},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {519--522},
     year = {2008},
     volume = {49},
     number = {3},
     mrnumber = {2490444},
     zbl = {1212.54100},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2008_49_3_a11/}
}
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Leiderman, A.; Protasov, I. V. Cellularity of a space of subgroups of a discrete group. Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 3, pp. 519-522. http://geodesic.mathdoc.fr/item/CMUC_2008_49_3_a11/