Geodesic
Cellularity of a space of subgroups of a discrete group
Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 3, pp. 519-522.

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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 $c(\Cal L(G))=\tau$.
Classification : 54A25, 54B20
Keywords: space of subgroups; cellularity; Shanin number 
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     title = {Cellularity of a space of subgroups of a discrete group},
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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/