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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On two problems concerning Baire sets in normal spaces


Author: Zoltán T. Balogh
Journal: Proc. Amer. Math. Soc. 103 (1988), 939-945
MSC: Primary 54C50; Secondary 54A35, 54D45
DOI: https://doi.org/10.1090/S0002-9939-1988-0947687-7
MathSciNet review: 947687
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0947687-7
Keywords: Baire versus Borel, Baire-ly perfectly normal, locally compact space
Article copyright: © Copyright 1988 American Mathematical Society