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In mathematics, Arakelyan's theorem is a generalization of Mergelyan's theorem from compact subsets of an open subset of the complex plane to relatively closed subsets of an open subset. == Theorem == Let Ω be an open subset of ℂ and ''E'' a relatively closed subset of Ω. By Ω * is denoted the Alexandroff compactification of ''Ω''. Arakelyan's theorem states that for every ''f'' continuous in ''E'' and holomorphic in the interior of ''E'' and for every ''ε'' > 0 there exists ''g'' holomorphic in Ω such that |''g'' − ''f''| < ''ε'' on ''E'' if and only if Ω * \ ''E'' is connected and locally connected. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Arakelyan's theorem」の詳細全文を読む スポンサード リンク
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