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