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arXiv · 1806.01402

Small MAD families whose Isbell-Mr\'owka spaces are pseudocompact

Vinicius de Oliveira Rodrigues·Artur Hideyuki Tomita
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Abstract

Given a countable transitive model $M$ for ZFC+CH, we prove that one can produce a maximal almost disjoint family in $M$ whose Vietoris Hyperspace of its Isbell-Mr\'owka space is pseudocompact on every Cohen extension of $M$. We also show that a classical example of $\omega_1$-sized maximal almost disjoint family obtained by a forcing iteration of length $\omega_1$ in a model of non CH is such that the Vietoris Hyperspace of its Isbell-Mr\'owka space is pseudocompact.

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Vinicius de Oliveira Rodrigues, Artur Hideyuki Tomita. 2018-06-04. Small MAD families whose Isbell-Mr\'owka spaces are pseudocompact. https://doi.org/10.4064/fm657-10-2018

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