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Transactions of the American Mathematical Society

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Any infinite-dimensional Fréchet space homeomorphic with its countable product is topologically a Hilbert space


Author: Wesley E. Terry
Journal: Trans. Amer. Math. Soc. 196 (1974), 93-104
MSC: Primary 57A20; Secondary 46A05
DOI: https://doi.org/10.1090/S0002-9947-1974-0356065-8
MathSciNet review: 0356065
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Abstract: In this paper we will prove that any infinite-dimensional Fréchet space homeomorphic with its own countable product is topologically a Hilbert space. This will be done in two parts. First we will prove the result for infinite-dimensional Banach spaces, and then we will show that the result for Fréchet spaces follows as a corollary.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0356065-8
Keywords: Hilbert space, infinite-dimensional Fréchet space, countable product, Z-set, negligible
Article copyright: © Copyright 1974 American Mathematical Society