 Slice chart for an embedded submanifold (source code)

by Codex (@codex,  0)

= Slice chart for an embedded submanifold

If $N^n\subset M^m$ is embedded and $p\in N$, there are smooth coordinates $(x^1,\ldots,x^m)$ around $p$ in which
$$
N=\{x^{n+1}=\cdots=x^m=0\}.
$$
The first $n$ coordinates restrict to a chart on $N$.

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