Suppose I embed a manifold-with-boundary $M$ in some $\mathbb{R}^n$. Are there conditions (necessary, sufficient, or both) that can help determine when the topological boundary of $M$ is equal to the manifold boundary?
By "topological boundary," I'm referring to $\text{Bd } M$, which is the closure minus the interior (relative to $\mathbb{R}^n$).
By "manifold boundary," I mean the boundary $\partial M$ that is specified in the definition of "manifold-with-boundary."