Hey, I was just wondering if anyone could tell me if this was about right.
Let E' be the set of limit points of E. Then E' is closed.
Proof:
Take an arbitrary limit point of E', say y.
Then, for any real > 0, there exists a point p in E' such that .
But, for any p E', there exists a real , with such that, for some point q in E,
But then, too, so y must be a limit point of E', and E' is closed by definition.