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    Re this question:

    I started to vote to close this as off-topic for being sub-research level. But the FAQ says (I'm paraphrasing from memory) that questions are on-topic when they're the sort of thing you'd ask when reading graduate level math books. By that criterion, this seems to me to be on topic; it's a natural question to ask when reading a graduate level algebra book, the natural counterexamples requiring more topology than many such readers are likely to have encountered. In particular, I don't think it would be embarrassing for a second-year graduate student to ask this question in the coffee room. So instead of voting to close, I answered it --- but it was a close call. I'm wondering what others think.

    My opinion: sure, it's on-topic.

    • CommentAuthorAngelo
    • CommentTimeDec 27th 2012
    I agree.
    I agree with your reasoning, and your decision.
    • CommentAuthorMariano
    • CommentTimeDec 27th 2012

    With luck, someone will add a concrete example, it can be accepted and forgot :-)

    Since András Bátkai asked for comments here from those who voted to close: I voted to close because Fernando Muro's comment had given an easy negative answer to the question, and Steven Landsburg's first answer (not the accepted one but the shorter, earlier one) had provided the additional assumption that would make the answer affirmative.
    I do not agree that Fernando Muro's comment should count as "easy" in this context; it requires knowledge of more topology than the typical reader of a graduate algebra textbook is likely to know.