Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



$ R$-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 $ R$-sets much in the spirit of Vaught and Burgess. Since the proofs entail many results on $ R$-sets and the $ R$-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 $ R$-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 $ R$-set and the other a Borel set. In fact, we prove a levelwise version of this result. For $ C$-sets, this has been proved by V. V. Srivatsa.

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Keywords: Positive analytical operations, $ \delta - s$ operation, inductive definability, game, $ R$-operator, $ R$-set
Article copyright: © Copyright 1984 American Mathematical Society