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 continuous function $g:|K|\to |L|$ 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.

Title	simplicial approximation theorem
Canonical name	SimplicialApproximationTheorem
Date of creation	2013-03-22 16:54:29
Last modified on	2013-03-22 16:54:29
Owner	Mathprof (13753)
Last modified by	Mathprof (13753)
Numerical id	5
Author	Mathprof (13753)
Entry type	Theorem
Classification	msc 55U10