Hartogs's theorem on separate holomorphicity: Difference between revisions

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{{about|a theorem on separate holomorphicity|a theorem on removableextensions of singularitiesholomorphic functions|Hartogs's lemmaextension theorem|a theorem on infinite ordinals|Hartogs number|a theorem on extensions of holomorphic functions|Hartogs's extension theorem}}

In [[mathematics]], '''Hartogs's theorem''' is a fundamental result of [[Friedrich Hartogs]] in the theory of [[several complex variables]]. Roughly speaking, it states that a 'separately analytic' function is continuous. More precisely, if <math>F:{\textbf{C}}^n \to {\textbf{C}}</math> is a function which is [[analytic function|analytic]] in each variable ''z''_''i'', 1 &le; ''i'' &le; ''n'', while the other variables are held constant, then ''F'' is a [[continuous function]].