Lie Groups Beyond an Introduction
《Lie Groups Beyond an Introduction》 · 印刷第 12 页 Introduction「Closed Linear Groups」，Theorem 0.15 前的 Lie group 定义段
A topological group whose underlying topology is that of a separable metric space will be called a separable topological group. A Lie group $G$ is a separable topological group with the additional structure of a smooth manifold compatible with the given topology in such a way that multiplication and inversion are smooth. Here multiplication is a mapping from $G\times G$ into $G$, and we understand $G\times G$ to be a smooth manifold whose charts are products of charts in the factors.