Measures on Suslinean spaces
Volume 235 / 2016
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.
