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Given $G$ a bounded domain, $f,g$, entire functions on whole $\overline{G}$

What is the meaning of $\overline{G}$? Is it the complement to the inside of the bounded domain?

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    I expect that it’s the closure of $G$.2012-09-13
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    Where did you read it?2012-09-13
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    What is the closure of G? I read it in German from an old exam sheet.2012-09-13
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    The closure is the smallest closed set containing $G$, which equals $G$ unioned with the set of limit points of $G$. http://en.wikipedia.org/wiki/Closure_(topology%292012-09-13
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    The all limit points of G dont they form $\partial G$ ? So $\overline{G} = G\cup \partial G$ ?2012-09-13
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    bakabakabaka: Every element of the boundary of $G$ is a limit point of $G$, but not every limit point is in the boundary. For example, every element of $G$ is a limit point of $G$ not in the boundary. However, your equation is correct, because every limit point not in $G$ is in the boundary. In fact, the boundary can be defined as the closure minus the interior, and the interior of an open set is the set itself.2012-09-13
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    The meaning of $\overline G$ now being clear, I'm still puzzled by "f,g entire functions on whole $\overline G$". Normally, an *entire function* means a function that is holomorphic on $\mathbb C$. So there is no point in saying "entire on ..." unless "entire" is actually a mistranslation.2012-09-14

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