I'm having a difficult time with this one. First off, $x$ is a condensation point of $A$ if every open nbhd $U$ of $x$ contains uncountably many points of $A$. Let us denote the set of condensation points as $A^c$ I have started a proof.

*Proof*. Let $X$ be a topological space and let $A \subset X$. We seek to show that $A^c$ is closed. To see this, we show that $X \setminus A^c$ is open.

Is this a good approach to the proof - to show closedness by showing openness of the complement? Also, I was wondering: does it follow that $X \setminus A^c$ contains only countably many points of $A$ or is that not the proper negation?