Talk:Hartogs' lemma

Is this stated correctly?
The page claims:
 * ''More precisely, on Cn for n ≥ 2, any analytic function F defined on the complement of a compact set K extends (necessarily uniquely) to an analytic function on Cn.

Suppose we take F(z)=1/z, defined on C\{0}, and let K={0}, which is certainly compact. Then F doesn't extend to an analytic function on C, unless the meaning of "analytic" is somehow extended beyond what I'm used to. --Trovatore 19:42, 23 October 2005 (UTC)
 * Sorry, I missed the condition n&ge;2. --Trovatore 19:44, 23 October 2005 (UTC)