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 called a 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 $a_{0}$ is a simplicial approximation of $f$.

Title simplicial approximation SimplicialApproximation 2013-03-22 16:54:24 2013-03-22 16:54:24 Mathprof (13753) Mathprof (13753) 6 Mathprof (13753) Definition msc 55U10