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I have read the book Function Theory of Several Complex Variables of Krantz. But there is a notation the meaning of which I don't know. The notation is $\subset\subset$. For example, "let $\Omega\subset\subset \mathbb{R}^{n}$ be a connected open set".

Can somebody give me a definition?

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As Zhen says, this notation usually means $\Omega$ is relatively compact in $R^n$. Why analysts tend to prefer this notation to saying "relatively compact in" or simply "bounded" if $R^n$ is involved will always remain a mystery to me... – t.b. Aug 11 '11 at 11:00

1 Answer 1

up vote 3 down vote accepted

There's an index of notation at the back of the book. Apparently, $\subset \subset$ means ‘relatively compact in’ and is defined in section 1.1.

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I have checked the index of notation of the book,but I don't find it.I just need some conclusions from this book,so I don't read this book carefully.Thank you for your help. – molan Aug 11 '11 at 9:02

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