simplicial approximation theorem

Let f:|K||L| be continuous functionMathworldPlanetmath, 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||L| such that g is a simplicial mapMathworldPlanetmath from K(s) to |L| and g is homotopicMathworldPlanetmath to f.

The theorem is due to J.W. Alexander.


  • 1 J.W. Alexander , Combinatorial analysis situs, Trans. Amer. Math. Soc. 28, 301-329, (1926)
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