Tell me more ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
up vote 1 down vote favorite

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 $\mathbb R$.

share|improve this question
3  
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
1  
@Brian: Perhaps you should write your comment as an answer? – mixedmath♦ May 6 '12 at 3:35
1  
@mixedmath: Done. (I too like to get questions off the Unanswered list.) – Brian M. Scott May 6 '12 at 3:39
show 1 more comment

1 Answer

up vote 2 down vote accepted

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.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.