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I know the following result:

If $X$ is a compact smooth manifold and $G$ is a compact Lie group which acts smoothly on $X$, then $X_G = (X\times EG)/G$ is a CW complex.

I don't know how to prove this result. Where can I find the proof? Thank you!

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    In this proposition, smooth manifold and smooth action may be necessary in some sense. Because when X is a local finite CW complex, X$\times$EG is a CW complex but the assertion is generally wrong.2011-04-15

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