(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove or disprove the following statement:

The closure of a set S is closed.

2. Relevant equations

Definition of closure: set T is the closure of set S means that T is the union of S and the set of limit points of S.

Definition of a closed set: set S is closed means that if p is a limit point of S then p is in S.

3. The attempt at a solution

So, the closure of set S-- call it set T-- contains all the elements of S and also all the limit points of S. Then, T must have limit points that is contained in it.

I can't prove that all the limit points of T is in T. I can only prove that all the limit points of S is in T. Help?

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# Homework Help: Analysis: the closure of a set is closed?

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