If 
is any space, then there is a CW-complex 
and a map 
inducing isomorphisms
on all homotopy, homology,
and cohomology groups.
CW-Approximation Theorem
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Cite this as:
Weisstein, Eric W. "CW-Approximation Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CW-ApproximationTheorem.html