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Measures on Suslinean spaces

Volume 235 / 2016

Piotr Borodulin-Nadzieja, Grzegorz Plebanek Fundamenta Mathematicae 235 (2016), 287-302 MSC: 03E35, 03E75, 28A60. DOI: 10.4064/fm229-3-2016 Published online: 5 August 2016

Abstract

We study the existence of nonseparable compact spaces that support a measure and are small from the topological point of view. In particular, we show that under Martin’s Axiom there is a nonseparable compact space supporting a measure which has countable $\pi $-character and which cannot be mapped continuously onto $[0,1]^{\omega _1}$. On the other hand, we prove that in the random model there is no nonseparable compact space having countable $\pi $-character and supporting a measure.

Authors

  • Piotr Borodulin-NadziejaInstytut Matematyczny
    Uniwersytet Wrocławski
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland
    e-mail
  • Grzegorz PlebanekInstytut Matematyczny
    Uniwersytet Wrocławski
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland
    e-mail

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