Is there a standard name for the closure of a submanifold of some fixed manifold M?
Example. The closed interval [0, 1] is not a manifold, because there is no atlas which contains charts at either 0 or 1. However, it is the closure of the manifold (0, 1) in the larger manifold ℝ.
Other Examples. The unit ball in ℝn for n>0 (the above example is isomorphic to the case n=1); the unit sphere in ℝn (which is itself already a manifold, but equal to its own closure in that embedding).
These objects may either have intrinsic boundary points, as with a closed interval, or lack them as with the unit sphere. They ought to have in common that removing their intrinsic boundary points (if any) leaves you with a submanifold of M, whose closure is the original set.
Is there standard terminology for such objects?