Given a spinning sphere, are the two mathematical points that represent the top and bottom of the sphere spinning, or stationary? Is there an equation that would prove either case? If a mathematical point has no dimensions, can it still spin?
What is your definition of "spinning"? I can't think of any definition that could apply to a point that is not moving; it would have to somehow identify different parts of the thing that is spinning, or directions within it, and a point has neither.
A spinning black hole has a dimensionless singularity which is presumably spinning. If a mathematical point can move through three dimensional geometry, why couldn't it spin in the same geometry? The two stationary points on the spinning sphere would spin at the same speed as the sphere itself, assuming that they are indeed spinning. If not, can this be shown mathematically?