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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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Homeomorphism groups of some direct limit spaces
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by Margie Hale PDF
Proc. Amer. Math. Soc. 85 (1982), 661-665 Request permission

Abstract:

Let $F$ be either of the spaces ${R^\infty } = {R^n}$ or ${Q^\infty } = {Q^n}$ where $R$ denotes the reals and $Q$ the Hilbert cube. Let $\mathcal {H}(M)$ be the homeomorphism group of a connected $F$-manifold $M$ with the compact-open topology. We prove that $\mathcal {H}(M)$ is separable, LindelΓΆf, paracompact, non-first-countable, and not a $k$-space.
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 85 (1982), 661-665
  • MSC: Primary 57S05; Secondary 54H15, 57N20, 58B05
  • DOI: https://doi.org/10.1090/S0002-9939-1982-0660625-4
  • MathSciNet review: 660625