For every topological space \(X\), there exists a CW complex \(Y\) and a weak homotopy equivalence \(f: X \to Y\). Moreover, if \(X\) is \(n{\hbox{-}}\)dimensional, \(Y\) may be chosen to be \(n{\hbox{-}}\)connected and is obtained from \(X\) by attaching cells of dimension greater than \(n\).