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
Explore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "CW-Approximation Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CW-ApproximationTheorem.html