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Keywords:
resolvability; irresolvability; Martin's Axiom; a space of weight less than $\frak C$
resolvability; irresolvability; Martin's Axiom; a space of weight less than $\frak C$
Summary:
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 ${\frak C}=\aleph_{\omega_1}$.
References:
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[He] Hewitt E.: A problem of set-theoretic topology. Duke Math. J. 10 (1943), 309-333. MR 0008692 | Zbl 0060.39407
[K] Kunen K.: Set Theory, The Introduction to Independence Proofs. North Holland Publ. Co. Amsterdam-New York, 1980. MR 0597342
[Ma] Malykhin V.I.: Extremaly disconnected and nearly extremaly disconnected groups. Soviet Math. Dokl. 16 (1975), 21-25.
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