On nonisomorphic analytic sets

Mauldin, R. Daniel

doi:10.1090/S0002-9939-1976-0431112-0

On nonisomorphic analytic sets
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by R. Daniel Mauldin PDF

Proc. Amer. Math. Soc. 58 (1976), 241-244 Request permission

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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