Degree of a Euclidean homeomorphism
= Degree of a Euclidean homeomorphism
{title2=$\deg(f:\mathbb R^n\to\mathbb R^n)$}
A Euclidean homeomorphism is a <proper map> and extends to its <one-point compactification> $S^n$. Its degree is the <degree of a continuous mapping> of this extension, and belongs to $\{1,-1\}$. A linear isomorphism has degree equal to the sign of its determinant.