-sets and category

Author:
Rana Barua

Journal:
Trans. Amer. Math. Soc. **286** (1984), 125-158

MSC:
Primary 04A15; Secondary 03D55, 03E15, 28A05, 54H05

MathSciNet review:
756034

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Abstract: We prove some category theoretic results for -sets much in the spirit of Vaught and Burgess. Since the proofs entail many results on -sets and the -operator, we have studied them in some detail and have formulated many results appropriate for our purpose in, perhaps, a more unified manner than is available in the literature. Our main theorem is the following: Any -set in the product of two Polish spaces can be approximated, in category, uniformly over all sections, by sets generated by rectangles with one side an -set and the other a Borel set. In fact, we prove a levelwise version of this result. For -sets, this has been proved by V. V. Srivatsa.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1984-0756034-6

Keywords:
Positive analytical operations,
operation,
inductive definability,
game,
-operator,
-set

Article copyright:
© Copyright 1984
American Mathematical Society