V.I. Malykhin
Irresolvable countable spaces of weight less than ${\frak C}$

Comment.Math.Univ.Carolinae 40,1 (1999) 181-185.

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