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
Canonical name	SimplicialApproximation
Date of creation	2013-03-22 16:54:24
Last modified on	2013-03-22 16:54:24
Owner	Mathprof (13753)
Last modified by	Mathprof (13753)
Numerical id	6
Author	Mathprof (13753)
Entry type	Definition
Classification	msc 55U10