Abstract: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 $.
Keywords: space of subgroups, cellularity, Shanin number
AMS Subject Classification: 54B20, 54A25