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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the characterization of Souslin and Borel sets
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by R.-D. Reiss
Proc. Amer. Math. Soc. 53 (1975), 530-534
DOI: https://doi.org/10.1090/S0002-9939-1975-0385827-2

Abstract:

Let $\mathfrak {X}$ be an arbitrary family of sets in the basic set $X$. In this paper Souslin-$\mathfrak {X}$ sets are represented as projections on $X$ of certain $\sigma \delta$-sets in the cartesian product space of $X$ and the Baire space (or $X$ and the real line). For $L{\text { - }}\mathfrak {X}$ sets (i.e. Souslin sets defined with disjoint unions; ensembles d’unicité) injective projections are considered. The results also apply to Borel-$\mathfrak {X}$ sets since the system of $L{\text { - }}\mathfrak {X}$ sets includes the Borel-$\mathfrak {X}$ sets under suitable conditions.
References
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Bibliographic Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 53 (1975), 530-534
  • MSC: Primary 54H05; Secondary 04A15
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0385827-2
  • MathSciNet review: 0385827