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What does $K \Subset U$ mean? I think that $K$ is a compact set with, $K \subset \subset U$ (precompact), where $U$ is an open set. Am I right? Thank you.

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The context would probably help. Did you see this in a book? A paper? Which one? – Zev Chonoles Jul 17 '12 at 20:45
Theorem 1.1 [here][1] [1]:… – user29999 Jul 17 '12 at 20:49
Yes, usually it means that $K$ has compact closure in $U$, see also: and looking at the link you gave I'm certain that's what is meant. – t.b. Jul 17 '12 at 20:51
I've always been under the impression that in analysis or PDE contexts, the difference between $\Subset$ and $\subset\subset$ is the difference of using $\langle,\rangle$ versus $<,>$, namely one of typography. (Or, perhaps a better example is using $<<$ versus $\ll$.) – Willie Wong Oct 9 '12 at 10:28

I have seen $K\subset\subset G$ if $K$ is compact, $G$ is open and $K\subseteq G$. I have seen it used in the context of locally compact topological spaces.

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