wild

Let $S$ be a set in ${ℝ}^n$ 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 $h:{ℝ}^n\to {ℝ}^n$ 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 bewild.

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