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

Alexandre Gabard

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

Alexandre Gabard

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Abstract

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.

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Alexandre Gabard. 2006-09-23. A separable manifold failing to have the homotopy type of a CW-complex. https://arxiv.org/abs/math/0609665

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