Sphere-sphere intersection is not a surface In my topology lecture, my lecturer said that when two spheres intersect each other, the intersecting region is not a surface. Well, my own understanding is that the intersecting region should look like two contact lens combine together,back to back. The definition of a surface that I have now is that every point has a neighbourhood which is homeomorphic to a disc. I don't see why the intersecting region is not a surface. It will be better if someone can guide me through picture. 

In general 2 spheres on $\mathbb{R}^3$ intersect on a circle which is a curve as you can simply imagine. You don't need to see a picture to visualize that I think..
