Lie Groups Beyond an Introduction
《Lie Groups Beyond an Introduction》 · 印刷第 73 页 Chapter I，Section 10「Elementary Theory of Lie Groups」，末段的局部同态定义；本书在解析群语境要求映射光滑、定义域为连通开邻域
If $G$ and $H$ are analytic groups, a local homomorphism of $G$ into $H$ is a pair $(\Psi,U)$, where $U$ is an open connected neighborhood of $1$ in $G$ and $\Psi:U\to H$ is a smooth map such that $\Psi(xy)=\Psi(x)\Psi(y)$ whenever $x$, $y$, and $xy$ are in $U$.