Arakelyan's theorem
Mathematical theorem From Wikipedia, the free encyclopedia
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 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.[1]
See also
References
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