# 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 |