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