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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Open subsets of $R^{\infty }$ are stable
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by Richard E. Heisey PDF
Proc. Amer. Math. Soc. 59 (1976), 377-380 Request permission

Abstract:

Let $U$ be an open subset of ${R^\infty } = \operatorname {dir} \lim {R^n}$, where $R$ denotes the reals. We show that $U \times {R^\infty }$ is homeomorphic to $U$. Combined with previous work of the author we obtain the corollary that two open subsets of ${R^\infty }$ are homeomorphic if and only if they have the same homotopy type.
References
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 59 (1976), 377-380
  • MSC: Primary 57A20; Secondary 58B05
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0425974-0
  • MathSciNet review: 0425974