Closedness of a set I am trying to understand closed sets.
Is the set
$$
A =\{x \in \mathbb{R}^2: \lVert x \rVert_2 \leq 1 \} -\{0\}
$$
closed?
I think it is not, because if we take the sequence $(\frac{1}{n})_{n=1}^{\infty}$ we can see it lies in A, but its limit is zero which is not in the set A. And because of that, A is not a closed set.
Is this right? Thank you.

Another way to see it is via the fact that closed sets are (perhaps defined as, depends on your definition of open set) the complements of open sets. The complement of $A$ is not open because there is no open ball of positive radius contained in $A^\complement$ around $(0,0)$
