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Let $M$ be a connected smooth manifold and $N$ a smooth manifold with boundary. If $f: M\to N$ is a smooth map of constant rank and there exists $p\in M$ such that $f(p)\in \operatorname{Int}N$, do we have $f(M)\subset \operatorname{Int}N$?

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  • $\begingroup$ Consider $\operatorname{id} : M \to M$ where $M$ is a smooth manifold with boundary. $\endgroup$ – Michael Albanese May 25 at 16:31

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