Abstract:We construct in Bell-Kunen's model: (a) a group maximal topology on a countable infinite Boolean group of weight $\aleph _1 < {\frak C}$ and (b) a countable irresolvable dense subspace of $2^{\omega _1}$. In this model ${\frak C}=\aleph _{\omega _1}$.
Keywords: resolvability, irresolvability, Martin's Axiom, a space of weight less than ${\frak C}$
AMS Subject Classification: Primary 54A35, 54E15, 20K45; secondary 54A25, 22A30