if $A$ is a subset of $\mathbb{R}^n$. Can I prove that "the set of all cluster points of A is closed" using the following:
- A closed subset is a subset that contains all its limit points.
- Every cluster point is a limit point (Not vice versa though).
- A has all cluster points means that it includes all its limits point and henceA is closed.
Is this an enough proof ?