Show that the subset of $\mathbb{R}^2$ given by $\{(x_1, x_2)\in \mathbb{R}^2:x_1>x_2\}$ is open.
Can anyone give me some help, or a proof for it. The book I'm using defines a subset $S$ of $E$ as open if for each $p\in S$, $S$ contains some open ball of center $p$.
Any input is appreciated.