Analytic Continuation and Riemann Surfaces
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Consider the following problem. Let f be an analytic function on a region G; when can f be extended to an analytic function f1 on an open set G1 which properly contains G? If G1, is obtained by adjoining to G a disjoint open set so that G becomes a component of G1,f can be extended to G1 by defining it in any way we wish on G1—G so long as the result is analytic. So to eliminate such trivial cases it is required that G1 also be a region.
KeywordsAnalytic Function Riemann Surface Topological Space Analytic Continuation Function Element
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