A separable manifold failing to have the homotopy type of a CW-complex

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We show that the Prüfer surface, which is a separable non-metrizable 2-manifold, has not the homotopy type of a CW-complex. This will follow easily from J. H. C. Whitehead's result: if one has a good approximation of an arbitrary space by a CW-complex, which fails to be a homotopy equivalence, then the given space is not homotopy equivalent to a CW-complex.
5 pages, 3 figures

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Geometric Topology, 57N05; 57Q05

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http://salesiana.dossiersoluciones.com/handle/123456789/116636

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0609665
 http://arxiv.org/abs/math/0609665

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arXiv