Recent content by hunhengy

I know this statement is right. The only thing is that I can not check it by the definition of Lie Group? Why should not need to check the maximal rank conditions of the $F_i$?

Recently, I read the follow paragraph: Let $G$ be a Lie group. If $H$ is a subgroup defined by the vanishing of a number of (continuous) real-valued functions $$H=\{g\in G| F_i(g)=0, i=1,2,\cdots,n\},$$ then $H$ is automatically a Lie subgroup of $G$. We do not need to check the maximal...