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Proceedings of the American Mathematical Society

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

 

 

On nonisomorphic analytic sets


Author: R. Daniel Mauldin
Journal: Proc. Amer. Math. Soc. 58 (1976), 241-244
MSC: Primary 54H05
MathSciNet review: 0431112
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Abstract: It is shown that if $ A$ is an analytic subset of $ I$, the unit interval, such that $ I - A$ is uncountable and does not contain a perfect set, then $ A$ is not Borel isomorphic to $ I \times A$ or to $ {A^n},n > 1$, or to $ U$, where $ U$ is a universal analytic subset of $ {I^2}$. It is also shown that $ U$ is not isomorphic to $ I \times A$ or to $ {A^n},n > 1$.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0431112-0
Keywords: Analytic sets, sieves, universal sets, Borel isomorphism, Axiom of Constructibility
Article copyright: © Copyright 1976 American Mathematical Society