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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Cantor tree, the $ \gamma$-property, and Baire function spaces


Author: Daniel K. Ma
Journal: Proc. Amer. Math. Soc. 119 (1993), 903-913
MSC: Primary 54C35; Secondary 03E35, 03E75, 54A35, 54E52
MathSciNet review: 1165061
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Abstract: Let $ X \subseteq {2^\omega }$ and $ T \cup X$ be the Cantor tree over $ X$. We show that $ {C_k}(T \cup X)$ is a Baire space if and only if $ X$ is a $ \gamma $-set. We obtain from this result consistent examples of spaces $ Y$ and $ Z$ such that $ {C_k}(Y)$ and $ {C_k}(Z)$ are Baire spaces but $ {C_k}(Y) \times {C_k}(Z)$ is not a Baire space. It also follows that there are consistent examples of locally compact nonparacompact spaces $ Y$ such that $ {C_k}(Y)$ is Baire but not weakly $ \alpha $-favorable.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1165061-X
PII: S 0002-9939(1993)1165061-X
Article copyright: © Copyright 1993 American Mathematical Society