Well, it's not clear to me why we would assume there is a boundary. And I don't know what it means to think of a 3D area as a 2D surface anyway. And I don't think it's possible to have a finite space with no well-defined boundary.
Oh. Yes, now that you have mentioned it, I do recall "space" being used in math classes in a unique way. It never occured to me that that is how "space" was being used.