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What does $\bar A$ denote when $ A \subseteq \mathbb{C}$?

I've seen it used in some places as the algebraic closure, other places as $\bar A = A$ \ $ \partial A $ and other places again as $\bar A = A$ \ $\{0\}$.

I should probably add that I don't expect it to be the algebraic closure in my context -- Cauchy's integral type stuff etc. etc.

sorry guys, I meant to write $\bar A = A \bigcup \partial A $ rather than $\bar A = A$ \ $ \partial A $. This turns out to be what is meant.

user27182
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    The symbol $\bar{\mathbb{C}}$ often denotes the Alexandroff compactification of a complex plane, i.e. the set $\mathbb{C}\cup {\infty}$, which extends $\mathbb{C}$ to a compact space. If you meant $\bar A$ for proper subsets $A\subset \mathbb{C}$, please consider editing title. – Kuba Helsztyński May 04 '13 at 08:45

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It depends on the context, but usually it means the topological closure of the set $A$.

(it could also mean the conjugate set of $A$, $\{ \bar{z} | z \in A \}$, so again, it totally depends upon context)

Fredrik Meyer
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  • @user27182: One usually says topological closure to distinguish it from other types of closures, for example from algebraic closures. Just a note: for most nice spaces, the notation $U \cup \partial U$ is the same as the topological closure. – Fredrik Meyer May 04 '13 at 09:24
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Most likely the topological closure, i.e. $\bar A = A \cup \partial A$. In some contexts, it could possibly mean the image of $A$ under the mapping $z \mapsto \bar z$.

By the way, I've never seen $\bar A = A \setminus \partial A$.

mrf
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