# Does this question provide enough information?

Suppose we are asked to prove that the quotient space $\mathbb R/\mathbb Z$ of $\mathbb R$ equipped with the quotient topology is compact. Has this question provided enough information for us to answer it? Do we not need to know the topology given to $\mathbb R$? I ask this because we can attach a wide variety of topologies to $\mathbb R$.

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You may assume that $\Bbb R$ has the usual (Euclidean) topology unless some other topology is specified. – Brian M. Scott May 5 '12 at 20:26
Yes, it is. If $\Bbb R$ were given the discrete topology, for instance, the quotient would be discrete and infinite and therefore not compact. – Brian M. Scott May 5 '12 at 20:30
@BrianM.Scott: Thank you. – sinclair May 5 '12 at 20:31
@Brian: Perhaps you should write your comment as an answer? – mixedmath May 6 '12 at 3:35
@mixedmath: Done. (I too like to get questions off the Unanswered list.) – Brian M. Scott May 6 '12 at 3:39
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You may generally assume that any $\Bbb R^n$ has the usual (Euclidean) topology unless some other topology is explicitly specified or made very clear by the context.