• Jun 6th 2008, 09:30 AM
Show that $S = \{ (x,y) \in \mathbb {R}^2 : xy > 1 \}$ and $C = \{ x \in \mathbb {R}^n : d(x,y) < 1 \ , \ y \in B$, B being any set, are open.
I understand that for both problems I need to pove that $D(x, t )$ are subsets of S and C for some positive number t. But, in the first one, I don't know how to get the y involve.
We don't know what $B$ is. Please tell us.