Any infinite-dimensional Fréchet space homeomorphic with its countable product is topologically a Hilbert space
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- by Wesley E. Terry
- Trans. Amer. Math. Soc. 196 (1974), 93-104
- DOI: https://doi.org/10.1090/S0002-9947-1974-0356065-8
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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.References
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Bibliographic Information
- © Copyright 1974 American Mathematical Society
- 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