Topological spaces that are -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 -favorable spaces introduced by G. Choquet [3]. For convenience, call the spaces mentioned in the title weakly -favorable. The following statements are true: (1) every dense subset of a quasi-regular, weakly -favorable space is weakly -favorable; (2) the product of any family of weakly -favorable spaces is weakly -favorable; (3) any continuous, open image of a weakly -favorable space is weakly -favorable; (4) a quasi-regular space with a -disjoint pseudo-base is weakly -favorable if and only if it is pseudo-complete in the sense of J. C. Oxtoby; and (5) the product of a weakly -favorable space and a Baire space is a Baire space.

**[1]**J. M. Aarts and D. J. Lutzer,*Completeness properties designed for recognizing Baire spaces*, Dissertationes Math. (Rozprawy Mat.)**116**(1974), 48. MR**0380745****[2]**J. M. Aarts and D. J. Lutzer,*Pseudo-completeness and the product of Baire spaces*, Pacific J. Math.**48**(1973), 1–10. MR**0326666****[3]**G. Choquet,*Lectures on analysis*. I:*Integration and topological vector spaces*, Benjamin, New York, 1969. MR**40**#3252.**[4]**John C. Oxtoby,*Cartesian products of Baire spaces*, Fund. Math.**49**(1960/1961), 157–166. MR**0140638****[5]**H. H. Wicke and J. M. Worrell Jr.,*Open continuous mappings of spaces having bases of countable order*, Duke Math. J.**34**(1967), 255–271. MR**0210084**

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DOI:
https://doi.org/10.1090/S0002-9939-1975-0367941-0

Keywords:
Weakly -favorable,
-favorable,
pseudo-complete,
-disjoint pseudo-base

Article copyright:
© Copyright 1975
American Mathematical Society