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A perfect set $A$ is one in which every point is a limit point. So it has to be closed. Does this mean that if we want to generate perfect sets inductively it is usually best to just intersect collections of other sets?

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    Well, $\mathbb{Q}$ is perfect but it isn't closed in $\mathbb{R}$.2011-08-23
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    I cannot see what this is asking...2011-08-23
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    It seems that the question rests on the assumption that a set in which every point is a limit point has to be closed, which, as Theo pointed out, is incorrect. The question doesn't make much sense without that assumption, so, in its own words, "it has to be closed".2011-08-23

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