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arXiv · 2112.03447

Submaximal spaces and cardinal invariants

César Corral
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Abstract

We give a combinatorial characterization of countable submaximal subspaces of $2^\kappa$. Using a parametrized version of Mathias forcing, we prove that there exists a countable submaximal subspace of $2^{\omega_1}$ whilst $\mathfrak{c}=\omega_2$. Combining this with previous results, we construct a disjointly tight countable irresolvable space of weight $<\mathfrak{c}$, answering a question of Bella and Hru\v{s}\'{a}k.

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César Corral. 2021-12-07. Submaximal spaces and cardinal invariants. https://arxiv.org/abs/2112.03447

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