Topology - Mathematics 362 - Fall 2007

1. In class we saw an equivalence relation ~ such that I x I / ~ is homeomorphic to a torus. Let J = [0,2] (the closed interval from 0 to 2).
   1. Find an equivalence relation R on J x J such that J x J / R is homeomorphic to a torus.
   2. Find a homeomorphism f : I x I / ~  --->  J x J / R. You do not need to prove your map f is a homeomorphism, but you must show it is well-defined.