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 bewild.

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

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