simplicial approximation

Let K and L be simplicial complexesMathworldPlanetmath and f:|K||L| be a continuous functionMathworldPlanetmath. A simplicial mapping g:|K||L| which is homotopicMathworldPlanetmath to f is called a simplicial approximation of f.

For example, suppose that L is the closurePlanetmathPlanetmath of an n-simplex and a0 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 a0 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