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

Show that

If S is totally bounded in ℂ, then the S closure is also totally bounded in ℂ.

2. Relevant equations

3. The attempt at a solution

Assume S is totally bounded. then for very ε>0 there are finitely many discs (O=Union of finitely many discs) that covers S let x be a limit points of S that is in S closure. but not in S.

hence x is in O (how can I show this?)

So x is in O for all x in S closure.

Hence S closure is totally bounded.

Am I on the right track?

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# Totally bounded sets

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