How many saddle points does a torus have?

Question

How many saddle points does a torus have?

Answer 1

A torus is a 3D donut - it either has an infinite number of saddle points or none.

http://en.wikipedia.org/wiki/Torus

Answer 2

When you ask about saddle points, usually you have a scalar function over some domain.  A torus is an (infinite) point set, not a function. So this question is a little bit ill-posed.  But you can define a function locally as each point---by using the tangent plane as the domain and the lifts of the points as the heights. Then, half of the torus (the inside half) are saddle points.