Geodesic
Irresolvable countable spaces of weight less than $\frak C$
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 1, pp. 181-185.

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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 ${\frak C}=\aleph_{\omega_1}$.
Classification : 20K45, 22A05, 22A30, 54A25, 54A35, 54E15, 54H05
Keywords: resolvability; irresolvability; Martin's Axiom; a space of weight less than $\frak C$ 
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Malykhin, V. I. Irresolvable countable spaces of weight less than $\frak C$. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 1, pp. 181-185. http://geodesic.mathdoc.fr/item/CMUC_1999__40_1_a13/