Without going into extreme depth A sphere is a 2D manifold since any point has a neighbourhood that looks more or less like 2D space.
A ball is like a 3D manifold for the same reason, but it also has some points where you don't have a neighbourhood that looks like 3D space but rather one that looks like half of 3D space. That region is the boundary, so to be exact a ball isn't a 3D manifold but a 3D manifold with boundary.
A ball is like a 3D manifold for the same reason, but it also has some points where you don't have a neighbourhood that looks like 3D space but rather one that looks like half of 3D space. That region is the boundary, so to be exact a ball isn't a 3D manifold but a 3D manifold with boundary.