If I have $\{ (x, 1/x) \in \mathbb{R}^n : 0 < x \leq 1 \}$, is this set closed?
I know that almost every point is a limit point (I drew the graph in the first quadrant), but should I test whether 0 has a neighbourhood that contains other points in the set? Or is it okay I can forget about it since it isn't even in the set anyways?