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Let A be a countable subset of [0,1]. Denote the set of accumulation points of A by A'. Can the set of accumulation points of A' be nonempty (i.e. can we have that A'' is nonempty)?

Thanks for your help

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  • $\begingroup$ Hint: What is the "simplest" countable subset of $[0,1]$? $\endgroup$ – njguliyev Oct 28 '13 at 21:09
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    $\begingroup$ yes, sorry, a very embarrassing question. but it has been answered so I cannot delete it :( $\endgroup$ – Frank Oct 28 '13 at 21:15
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HINT: Take $A=\Bbb Q\cap[0,1]$.

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