TITLE: Are non-PL manifolds CW-complexes?
QUESTION [26 upvotes]: 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.

REPLY [15 votes]: 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.

REPLY [7 votes]: See http://arxiv.org/abs/math/0609665