Can every topological (not necessarily smooth or PL) manifold be given the structure of a CW complex?
I'm pretty sure that the answer is yes. However, I have not managed to find a reference for this.
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Sign up to join this communityCan every topological (not necessarily smooth or PL) manifold be given the structure of a CW complex?
I'm pretty sure that the answer is yes. However, I have not managed to find a reference for this.
Kirby and Siebenmann's paper "On the triangulation of manifolds and the Hauptvermutung" Bull AMS 75 (1969) is the standard reference for this, I believe.
The result is that compact topological manifolds have the homotopy-type of CW-complexes, to be precise.