On two problems concerning Baire sets in normal spaces

Balogh, Zoltán T.

doi:10.1090/S0002-9939-1988-0947687-7

On two problems concerning Baire sets in normal spaces
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Proc. Amer. Math. Soc. 103 (1988), 939-945 Request permission

Abstract:

Two problems will be dealt with. The first problem, due to Katetov, asks whether there is a normal, nonperfect ${T_2}$ space $X$ such that the Baire and Borel algebras in $X$ coincide. The second problem, due to Ross and Stromberg, asks whether each closed Baire set has to be zero set in a normal, locally compact ${T_2}$ space. Several consistent examples of spaces satisfying the requirements of the first problem will be constructed. A counterexample to the second problem is given in ZFC.

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