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$\begingroup$

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?2012-07-17
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    Theorem 1.1 [here][1] [1]: http://www.msri.org/attachments/workshops/563/563_Lecture-notes_Petrosyan.pdf2012-07-17
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    Yes, usually it means that $K$ has compact closure in $U$, see also: http://mathoverflow.net/questions/43950/meaning-of-subset-notation and looking at the link you gave I'm certain that's what is meant.2012-07-17
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    See: http://math.stackexchange.com/questions/50253/subset-vs-subseteq-when-not-referring-to-strict-inclusion/50256#comment112665_502562012-07-17
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    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 $\ll$.)2012-10-09

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