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glmuelle

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I'm trying to solve this exercise

"Prove that if C is a circular cylinder with S_1 and S_2 as its boundary circles and S_1 and S_2 are identified by mapping them both homeomorphically onto some third circle S, giving a map [tex] f: S_1 \cup S_2 \rightarrow S[/tex] then [tex] (C - S_1 \cup S_2) \cup S[/tex] with the identification topology (induced by the function that identifies all the points in S_1 and S_2 with corresponding points in S) is a torus."

Is it enough to show that the topology on [tex] (C - S_1 \cup S_2) \cup S[/tex] is the subspace topology of R^3?

Thanks for your help