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  • Function spaces of CW homotopy type are Hilbert manifolds
    Smrekar, Jaka ; Yamashita, Atsushi
    Let▫$X$▫ be a countable CW complex and ▫$Y$▫ an ANR (for metric spaces) and ▫$Y^X$▫ 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.
    Source: Proceedings of the American Mathematical Society. - ISSN 0002-9939 (Vol. 137, no. 2, 2009, str. 751-759)
    Type of material - article, component part
    Publish date - 2009
    Language - english
    COBISS.SI-ID - 14965849

    Link(s):

    http://dx.doi.org/10.1090/S0002-9939-08-09584-1

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