Search found 2 matches
- Thu Oct 12, 2017 8:07 am
- Forum: Real Analysis
- Topic: Open subset
- Replies: 3
- Views: 4445
Re: Open subset
Welcome
- Thu Oct 05, 2017 9:49 pm
- Forum: Real Analysis
- Topic: Open subset
- Replies: 3
- Views: 4445
Re: Open subset
Since $G$ is non empty, let $a \in \displaystyle{\mathbb{R}}$ be a real that belongs to $G$. But then, $a-a$ must also belong to $G$, that is, $0 \in G. \\$ Now since $G$ is open, there must exist an open interval around $0$, say $(-\delta,\delta) \subseteq G$ with $\delta >0$. Now pick any positive...