# wild

Let $S$ be a set in ${\mathbb{R}}^{n}$ and suppose that $S$ is triangulable.
($S$ is *triangulable* means that when regarded as a space, it has a triangulation.)

If there is a homeomorphism^{} $h:{\mathbb{R}}^{n}\to {\mathbb{R}}^{n}$ such that
$h(S)$ is a polyhedron, we say that $S$ is *tamely imbedded*.

If $S$ is triangulable but no such homeomorphism exists $S$ is said to be
*wild*.

In ${\mathbb{R}}^{2}$ every 1-sphere is tamely imbedded. But in ${\mathbb{R}}^{3}$ there are wild arcs, 1-spheres and 2-spheres.

Title | wild |
---|---|

Canonical name | Wild |

Date of creation | 2013-03-22 16:52:54 |

Last modified on | 2013-03-22 16:52:54 |

Owner | Mathprof (13753) |

Last modified by | Mathprof (13753) |

Numerical id | 8 |

Author | Mathprof (13753) |

Entry type | Definition |

Classification | msc 55S37 |

Defines | tamely imbedded |

Defines | triangulable |