Cellularity of a space of subgroups of a discrete group Academic Article uri icon

abstract

  • Abstract. 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.

publication date

  • January 1, 2008