= Hartogs extension theorem
{c}
{title2=$\mathcal O(B\setminus\{0\})=\mathcal O(B)$ for $\dim_{\mathbb C}B\geq2$}
{wiki=Hartogs's_extension_theorem}
= Hartogs's extension theorem
{c}
{synonym}
In complex dimension at least two, a holomorphic function on a punctured coordinate ball extends holomorphically through its centre. Componentwise extension in a <holomorphic local frame> gives the same statement for <holomorphic sections>. This preserves global sections after removing finitely many points, but does not imply preservation of higher <sheaf cohomology>. This analytic theorem differs from the set-theoretic <Hartogs theorem>.
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