# 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 Wild 2013-03-22 16:52:54 2013-03-22 16:52:54 Mathprof (13753) Mathprof (13753) 8 Mathprof (13753) Definition msc 55S37 tamely imbedded triangulable