In response to this question, is it true that for $f:\mathbb{C}-A\to \mathbb{C}$ analytic where $A$ is countable (but not closed!) that $f$ bounded implies $f=c$?
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oops, $A$ should be countable. – edo arad Jul 28 '13 at 18:54
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1Analytic functions are defined on open sets, so $A$ needs to be closed. – Ayman Hourieh Jul 28 '13 at 18:55
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Thanks! I should have figured it out.. – edo arad Jul 28 '13 at 18:56
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I think you could have left it as an answer – edo arad Jul 28 '13 at 18:57
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Edited and undeleted. My previous answer was for uncountable $A$. – Ayman Hourieh Jul 28 '13 at 18:58
