A space with only Borel subsets

2000/09/05 by Saharon Shelah, Shelah, Saharon
Mathematics · #Advanced Topology and Set Theory #math.GN #math.LO

paper · pdf · doi:10.48550/arxiv.math/0009047

published as Period. Math. Hungar. 40 No. 2 (2000) 81--84

arxiv created 2000/09/05 · arxiv updated 2009/11/30

Abstract

Miklos Laczkovich asked if there exists a Haussdorff (or even normal) space in which every subset is Borel yet it is not meager. The motivation of the last condition is that under MA_kappa every subspace of the reals of cardinality kappa has the property that all subsets are F_sigma, however Martin's axiom also implies that these subsets are meager. Here we answer Laczkovich' question.

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