I need to prove that the set $C=\{ (x,y)\in \mathbb R^2|xy=1\} $ is closed in $\mathbb R^2$
I tried to prove it by proving that complement of $C$ in $\mathbb R^2$ is open ? Is it enough to show that for every $(x,y)$ not in $C$, $\exists r>0$ s.t. $B_r(x,y)\cap C=\emptyset$, where $B_r$ is a ball centered at (x,y) ?
Best Answer
Not only is it enough, one might say that is exactly what is required.