= Cellular approximation theorem
{wiki=Cellular_approximation}
= Cellular approximation
{synonym}
A <continuous map> between <CW complexes> is homotopic to a <cellular map>. If the map is already cellular on a subcomplex, the homotopy can be taken relative to that subcomplex. In particular, a map from a $d$-dimensional <CW complex> can be deformed into the $d$-skeleton of the target. This permits finite <cellular chain complexes> to compute induced <homology> maps, and turns maps to <Complex projective space> into maps to an appropriate finite-dimensional projective skeleton.
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