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

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

2006-09-23

arxiv.org/abs/math/0609665v1

Mathematics

Geometric Topology

5 pages, 3 figures

Scientific paper

We show that the Pr\"ufer 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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