# Topology exercise.

• Oct 20th 2012, 12:37 AM
vercammen
Topology exercise.
Picture attached.
• Oct 20th 2012, 05:20 AM
Plato
Re: Topology exercise.
Quote:

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?
• Oct 30th 2012, 11:46 PM
vercammen
Re: Topology exercise.
I expect any kind of help. Even hint or the first step.
Anyway, here is what I got

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

2. We consider the real line with usual topology, $\displaystyle A:=(0,1)$ and $\displaystyle G:=\{0\}$. The LHS is $\displaystyle \{0\}$ but the RHS is empty.
• Nov 19th 2012, 07:30 PM
wallisonline
Re: Topology exercise.
What are some good books for a layperson who wants to teach himself set theory?

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