I forget for a while, we don't need the compactness condition here right?
Does noncompact manifold or orbifold have the homotopy type,of CW complex?
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algebraic-topology
homotopy-theory
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0Relevant comments and references can be found on MO also http://mathoverflow.net/questions/36838/are-non-pl-manifolds-cw-complexes even though the question is not exactly the same. – 2012-04-14