simplicial approximation

Let $K$ and $L$ be simplicial complexes and $f:|K|\to |L|$ be a continuous function.A simplicial mapping $g:|K|\to |L|$ which is homotopic to $f$ is calleda simplicial approximation of $f$.

For example, suppose that $L$ is the closure of an $n$-simplex and $a_0$ is a vertex of $L$. Let $f$ be a continuous map of $|K|$ to $|L|$ where $K$is some simplicial complex. Then the map $g$ that sends all of $K$ to $a_0$ isa simplicial approximation of $f$.