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 Post subject: Closed and compact
PostPosted: Wed Jun 08, 2016 4:31 pm 
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Joined: Mon Nov 09, 2015 1:52 pm
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Let \(\displaystyle{X}\) be a topological vector space, \(\displaystyle{K\subseteq X}\) a compact

subset of \(\displaystyle{X}\) and \(\displaystyle{C\subseteq X}\) a closed subset of \(\displaystyle{X}\)

such that \(\displaystyle{K\cap C=\varnothing}\).

Then, there exists an open region \(\displaystyle{V}\) of \(\displaystyle{0\in X}\) such that

\(\displaystyle{(K+V)\cap (C+V)=\varnothing}\)


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