# Do we have $f(M)\subset \operatorname{Int}N$?

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 $$f(M)\subset \operatorname{Int}N$$?

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