Originally Posted by Leo Bloom
Then does topology not deal with surfaces (or surface sets) enclosing other surface sets?
Please excuse the grade-school questions.
It does, but discrete surfaces (and in the mathematical/geometrical study, usually idealized, abstract ones). So, we really would have to break the body down into as many discrete "objects" as possible. But as an highly complex organism, this is virtually impossible and full of gray areas to take it out of a topological context.
That said, you can sever the eyeball from its nerve, blood supply and muscles, then say, topologically, the surface is a 2-sphere, but the iris inside is a torus.
We all know the skin is full of thousands of pours, the lungs are full a millions of alveoli, and even the circulatory system is a mind-fuck if you go all the way down to the capillary level.
So, saying topologically a human is a torus based on the GI track alone barely cuts it. Where does the GI track begin and end?