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jostpuur
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Is it possible for a complex analytic function to have an uncountable set of singular points?
HallsofIvy said:Analytic where? Obviously, a function that is analytic everywhere has NO singular points. Am I correct that by "singular point" you mean a point at which the function is not analytic?
Certainly it would be possible to define a function that would be analytic everywhere except at certain points and I see no reason why one could not do that for and uncountable set of points. The only requirement would be that the set of points on which the function is not analytic would be a closed set.
mathwonk said:it depends what kind of functions you want to allow. you want of course a function which is analytic on some open, presumably connected set in C, and which cannot be analytically continued outside that set to another strictly larger such open connected set, right?