I think the confusion here is that you're taking what he's saying in terms other than those of topology. In topology, you deal with manifolds. Manifolds have n

I think the confusion here is that you're taking what he's saying in terms other than those of topology. In topology, you deal with manifolds. Manifolds have no thickness, but they do have area. In topology, there's no such thing as a 'filled' sphere: a sphere in topology has no edges and an inside surface and an outside surface, much like a football. There are two ways you can make a 'bottle': you can deform a sphere, which gives you a 'bottle' much like a vaccuum flask; or you can deform a planar manifold (which is like a sheet of paper). The former will have two surfaces and no edge, whereas the latter will have two surfaces and one edge, that being the rim. A broken sphere would be a planar manifold. A vaccuum flask is simply a deformed sphere in topological terms, and thus only has two surfaces, the inside and the outside.