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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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Function spaces of CW homotopy type are Hilbert manifolds
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by Jaka Smrekar and Atsushi Yamashita PDF
Proc. Amer. Math. Soc. 137 (2009), 751-759 Request permission

Abstract:

Let $X$ be a countable CW complex and $Y$ an ANR (for metric spaces) and let $Y^X$ denote the space of continuous maps from $X$ to $Y$ with the compact-open topology. We show that, under mild restrictions, the following are equivalent: (1) $Y^X$ is an $\ell ^2$-manifold, (2) $Y^X$ is an ANR, (3) $Y^X$ has the homotopy type of a CW complex. We also give a few interesting examples and applications.
References
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Additional Information
  • Jaka Smrekar
  • Affiliation: Fakulteta za Matematiko in Fiziko, Jadranska ul. 19, SI-1111 Ljubljana, Slovenia
  • Email: jaka.smrekar@fmf.uni-lj.si
  • Atsushi Yamashita
  • Affiliation: Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1, Komaba, Meguro-ku, Tokyo 153-8914, Japan
  • Email: yonster@ms.u-tokyo.ac.jp
  • Received by editor(s): February 1, 2008
  • Published electronically: August 28, 2008
  • Additional Notes: The first author was supported in part by the ARRS research project No. J1-6128-0101-04.
    The second author was supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists.
  • Communicated by: Alexander N. Dranishnikov
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 751-759
  • MSC (2000): Primary 54C35; Secondary 55M15, 57N20
  • DOI: https://doi.org/10.1090/S0002-9939-08-09584-1
  • MathSciNet review: 2448598