A space with only Borel subsets
Logic
2007-05-23 v1 General Topology
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.
Cite
@article{arxiv.math/0009047,
title = {A space with only Borel subsets},
author = {Saharon Shelah},
journal= {arXiv preprint arXiv:math/0009047},
year = {2007}
}