Given a discrete group G, we consider the set L(G) of all subgroups of G endowed with topology of pointwise convergence arising from the standard embedding of L(G) into the Cantor cube (0, 1)G. We show that the cellularity c(L(G)) ≤ ℵ0 for every abelian group G, and, for every infinite cardinal τ we construct a group G with c(L(G)) =τ.
|Number of pages||4|
|Journal||Commentationes Mathematicae Universitatis Carolinae|
|State||Published - 1 Jan 2008|
- Shanin number
- Space of subgroups
ASJC Scopus subject areas
- Mathematics (all)