Let S be a set in 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 homeomorphismMathworldPlanetmath h:nn 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 2 every 1-sphere is tamely imbedded. But in 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