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I'm having trouble proving the following statement: Assume X is a second countable topological space and let $A^c$ denote the condensation points of a given set, $A$ (i.e, those points such that for any neighbourhood of the point, the nbd intersection A is non countable). I want to prove that $A-A^c$ is non countable.

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    $\begingroup$ ?? What if $X=A=[0,1]?$ $\endgroup$ – zhw. Mar 26 '17 at 17:18
  • $\begingroup$ Other counter-examples: $X=A=\mathbb R,$ or $X=\mathbb R$ and $A=\mathbb R$ \ $\mathbb Q.$ In either case we have $A^c=X.$ $\endgroup$ – DanielWainfleet Mar 26 '17 at 20:42

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