>>12337019Start with giving each point of a grid a point on another surface.
That's basically everything.
Count how many holes it does, and for same number of holes it's homeomorphic.
Poincare was idiot, and doesn't know that if you map a torus on a sphere, you'll have exactly one filled circle of points of size of one points remaining unfilled in circle and you cannot close them to one sphere and sphere has unite number of points infinite and evenly distributed, therefore if you map torus, it won't fully close because one point is remaining because circle cannot shrink to one point but has point in the middle otherwise it's not a cricle even at r=0.