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Function Spaces of CW Homotopy Type Are Hilbert Manifolds

Jaka Smrekar and Atsushi Yamashita
Proceedings of the American Mathematical Society
Vol. 137, No. 2 (Feb., 2009), pp. 751-759
Stable URL: http://www.jstor.org/stable/20535793
Page Count: 9
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Function Spaces of CW Homotopy Type Are Hilbert Manifolds
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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 ℓ²-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.

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