## Minimal Jordan domain

I am trying to find and define the smallest Jordan domain G′ containing a simply connected bounded domain G in the complex plane. It seems that $G'=\bigcap_{H\supset G} H$, where $H$ is a Jordan domain but I have not the proof.

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 This also looks like homework, and will suffer the fate of your other question. math.SE is the right place for this sort of thing, or at least a better place. – Igor Rivin Nov 26 2011 at 22:28 Not sure this is homework, but I otherwise agree with Igor. I recommend looking at the links I left in comments on your previous question – Yemon Choi Nov 26 2011 at 22:46 Homework or not homework, you know the lakes of Wada. Note that removing any two lakes during any finite day gives you a Jordan domain surrounding the third but in the end you have a crazy boundary, so your statement is false. – fedja Nov 26 2011 at 23:26 This is what @fedja is talking about: en.wikipedia.org/wiki/Lakes_of_Wada – Igor Rivin Nov 27 2011 at 10:19