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.
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.