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Compact $ \mathcal{G}$-souslin sets are $ G_\delta$'s


Author: Eric John Braude
Journal: Proc. Amer. Math. Soc. 40 (1973), 250-252
MSC: Primary 54H05
DOI: https://doi.org/10.1090/S0002-9939-1973-0321047-3
MathSciNet review: 0321047
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Abstract: The result of the title generalizes and places in a new set-theoretical context the well-known theorem of Halmos that every compact Baire set is a $ {\mathcal{G}_\delta }$. Šneĭder's result of 1968 that every perfectly normal compact space with $ \mathcal{G}$-Souslin diagonal is metrizable, can now be seen to be true without the perfect normality condition.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0321047-3
Keywords: Souslin, compact, $ {\mathcal{G}_\delta }$, second countable
Article copyright: © Copyright 1973 American Mathematical Society

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