Complex Variables

**LCopper2010** · February 4th 2010, 11:12 AM

Prove that if a set contains each of its accumulation points, then it must be a closed set.

**Plato** · February 4th 2010, 11:57 AM

Originally Posted by LCopper2010

Prove that if a set contains each of its accumulation points, then it must be a closed set.

Suppose that $\mathcal{A}$ is such a set.
If $x\in\mathcal{A}^c$ , the complement, then $x$ is not a limit point of $\mathcal{A}$ .
Therefore, the is an open set, $x\in\mathcal{O}_x$ that contains no point of $\mathcal{A}$ .
Now show the complement is open.

**HallsofIvy** · February 5th 2010, 04:12 AM

What does this have to do with complex variables?

Thread: Complex Variables

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