# Let S1 be the unit circle with the usual topology, S1 × S1 be the product...

Let S1 be the unit circle with the usual topology, S1 × S1 be the product space, and define the torus T : = [0,1] × [0,1] / ∼ as a quotient space, where ∼ is the equivalence relation that (1,y) ∼ (0,y) for all y ∈ [0,1] and (x,0) ∼ (x,1) for all x ∈ [0,1]. Prove that S1 × S1 and T are homeomorphic.

Let Sl be the unit circle with the usual topology, Stx St be the product space, and define the torus T := [0,1] [0,1]/ -as a quotient space, where is the equivalence relation that (1, y) (0,y) for all y € (0,1) and (1,0) (1,1) for all € [0,1]. Prove that Six Stand T are homeomorphic.

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