MathGloss

Let $m< n$. Then an $m$-dimensional smooth manifold embedded in $\mathbb R^n$ with boundary is a subset $M \subset\mathbb R^n$ such that for all points $p \in M$, there exists an open set $U \subset H^k$ the closed half-space and an open neighborhood $V \subset M$ of $p$ and a map $\phi: U \to V$ such that

1. $\phi$ is a homeomorphism
2. $\phi$ is smooth in $H^k$ ( todo: what is this exactly?)
3. the total derivative $D\phi(x)$ has rank $m$ for all $x \in U$.

Wikidata ID: Q1333611

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