Measures on Suslinean spaces

2015/11/16 by Borodulin-Nadzieja, Piotr, Plebanek, Grzegorz
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1511.04979

Abstract

We study the existence of non-separable 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 non-separable compact space supporting a measure which has countable π-character and which cannot be mapped continuously onto [0,1]^ω₁. On the other hand, we prove that in the random model there is no non-separable compact space having countable π-character and supporting a measure.

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