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Small MAD families whose Isbell--Mr\'owka space has pseudocompact hyperspace

Volume 247 / 2019

Vinicius de Oliveira Rodrigues, Artur Hideyuki Tomita Fundamenta Mathematicae 247 (2019), 99-108 MSC: Primary 54B20, 54D80; Secondary 54D20, 54A35. DOI: 10.4064/fm657-10-2018 Published online: 30 May 2019

Abstract

We prove that it is consistent that there exists a MAD family $\mathcal A$ of cardinality $\omega _1 \lt \mathfrak c$ such that the Vietoris hyperspace of its Isbell–Mrówka space, ${\rm CL} (\varPsi (\mathcal A))$, is pseudocompact. In the same model, there exist MAD families $\mathcal A_1, \mathcal A_2$ such that ${\rm CL} (\varPsi (\mathcal A_1))$ is pseudocompact but ${\rm CL} (\varPsi (\mathcal A_2))$ is not.

Authors

  • Vinicius de Oliveira RodriguesInstitute of Mathematics and Statistics
    University of São Paulo
    Rua do Matão, 1010, São Paulo, Brazil
    e-mail
  • Artur Hideyuki TomitaInstitute of Mathematics and Statistics
    University of São Paulo
    Rua do Matão, 1010, São Paulo, Brazil
    e-mail

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