The torus,Tcan be obtained as an identification space as

follows: Let X = [0,1] x [0,1] denote the square, and define an equivalence relation on X by (0,t) ~(1,t) and (s,0) ~(s,1) for all s,t in [0,1].

Prove carefully that X/~is a closed 2-manifold

Prove that X is homeomorphic to S1 x S1 where S1 is the circle

Any help would be great. Thanks