simplicial approximation theorem

Let $f:|K|\to |L|$ be continuous function, where $|K|$ and $|L|$are polyhedra having triangulations $K$ and $L$, respectively.

Then there is a barycentric subdivision $K^{(s)}$ of $K$ and a continuousfunction $g:|K|\to |L|$ such that $g$ is a simplicial map from $K^{(s)}$to $|L|$ and $g$ is homotopic to $f$.

The theorem is due to J.W. Alexander.