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'wild'
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| Title of object: |
wild |
| Canonical Name: |
Wild |
| Type: |
Definition |
| Created on: |
2007-03-31 09:12:35 |
| Modified on: |
2007-03-31 09:12:35 |
| Classification: |
msc:55S37 |
| Defines: |
tamely embedded |
Preamble:
% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%\usepackage{xypic}
% there are many more packages, add them here as you need them
% define commands here
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Content:
Let $S$ be a set in ${\mathbb{R}}^n$ and suppose that $S$ is triangulable.
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 \emph{tamely embedded}.
If $S$ is triangulable but no such homeomorphism $S$ is said to be
\emph{wild}.
In ${\mathbb{R}}^2$ every 1-sphere is tamely embedded. But in
in ${\mathbb{R}}^3$ there are wild arcs, 1-spheres and 2-spheres.
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