A space with only Borel subsets
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 MAkappa every subspace of the reals of cardinality kappa has the property that all subsets are Fsigma, however Martin's axiom also implies that these subsets are meager. Here we answer Laczkovich' question.
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