# Math Help - Topology exercise.

1. ## Topology exercise.

Picture attached.

2. ## Re: Topology exercise.

Originally Posted by vercammen
Picture attached.
You have posted an attachment without any comment whatsoever.
Do you expect someone to do the problem(s) for you?

3. ## Re: Topology exercise.

I expect any kind of help. Even hint or the first step.
Anyway, here is what I got

1. Clearly $\supset$ is always true, even when $G$ is not open. Let $x\in \overline{G\cap \overline A}$, and $O$ an open neighborh. of $x$. It necessarily meets a point of $G\cap \overline A$, say $y$. As $y\in\overline A$, and $G$ is a neighborhood of $y$, $G\cap A\cap O\neq \emptyset$. So $x\in \overline{G\cap A}$.

2. We consider the real line with usual topology, $A:=(0,1)$ and $G:=\{0\}$. The LHS is $\{0\}$ but the RHS is empty.

4. ## Re: Topology exercise.

What are some good books for a layperson who wants to teach himself set theory?

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