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Two unrelated results involving Baire spaces

Author: H. E. White
Journal: Proc. Amer. Math. Soc. 44 (1974), 463-466
MSC: Primary 54E99
MathSciNet review: 0346761
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Abstract: Two results are obtained in this paper. The first is a generalization of J. C. Oxtoby's category analogue of the Kolmogoroff zero-one law. The second result: every dense $ {G_\delta }$ subset of a quasi-regular $ \alpha $-favorable space is $ \alpha $-favorable.

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  • [1] G. Choquet, Lectures on analysis. Vol. I: Integration and topological vector spaces, Benjamin, New York, 1969. MR 40 #3252. MR 0250011 (40:3252)
  • [2] J. C. Oxtoby, Cartesian products of Baire spaces, Fund. Math. 49 (1960/61), 157-166. MR 25 #4055; 26, 1453. MR 0140638 (25:4055)
  • [3] M. Bhaskara Rao and K. P. S. Bhaskara Rao, A category analogue of Hewitt-Savage zero-one law, Proc. Amer. Math. Soc. 44 (1974), 497-499. MR 0345084 (49:9823)
  • [4] H. E. White, Jr., Topological spaces that are $ \alpha $-favorable for a player with perfect information, Proc. Amer. Math. Soc. (to appear).

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Keywords: Tail set, zero-one law, weakly $ \alpha $-favorable, property of Baire, $ \alpha $-favorable, pseudo-complete
Article copyright: © Copyright 1974 American Mathematical Society

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