$R$-sets and category
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- Trans. Amer. Math. Soc. 286 (1984), 125-158 Request permission
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.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 286 (1984), 125-158
- MSC: Primary 04A15; Secondary 03D55, 03E15, 28A05, 54H05
- DOI: https://doi.org/10.1090/S0002-9947-1984-0756034-6
- MathSciNet review: 756034