$S= \{ (x,y)\in \mathbb{R^2}: x^2 + y^2 = \frac{1}{n^2}, n \in \mathbb{N}$
Help me determine wether the set is closed,open, bounded or compact.
Determining if the set is bounded is trivial, but I am having some trouble determining if the set is closed, open or any of them. I'm pretty sure that the point $(0,0)$ can cause some troubles.
Thanks in advance
The set $S$ is not closed as the origin is a limit point of $S$ that doesn't belong to $S$.
$S$ is not open as you can't find an open ball centered on $(1,0) \in S$ that is included in $S$.