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

 

Topological spaces that are $ \alpha $-favorable for a player with perfect information


Author: H. E. White
Journal: Proc. Amer. Math. Soc. 50 (1975), 477-482
MSC: Primary 54E99; Secondary 54C50
MathSciNet review: 0367941
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Abstract: The class of spaces mentioned in the title is closely related to the class of $ \alpha $-favorable spaces introduced by G. Choquet [3]. For convenience, call the spaces mentioned in the title weakly $ \alpha $-favorable. The following statements are true: (1) every dense $ {G_\delta }$ subset of a quasi-regular, weakly $ \alpha $-favorable space is weakly $ \alpha $-favorable; (2) the product of any family of weakly $ \alpha $-favorable spaces is weakly $ \alpha $-favorable; (3) any continuous, open image of a weakly $ \alpha $-favorable space is weakly $ \alpha $-favorable; (4) a quasi-regular space with a $ \sigma $-disjoint pseudo-base is weakly $ \alpha $-favorable if and only if it is pseudo-complete in the sense of J. C. Oxtoby; and (5) the product of a weakly $ \alpha $-favorable space and a Baire space is a Baire space.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0367941-0
PII: S 0002-9939(1975)0367941-0
Keywords: Weakly $ \alpha $-favorable, $ \alpha $-favorable, pseudo-complete, $ \sigma $-disjoint pseudo-base
Article copyright: © Copyright 1975 American Mathematical Society