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let $f$ be a complex valued function. if $f$ has uncountable number of singularity.

Then is it true that $f$ must have non isolated singularity ??

I think it is true . but have no idea how to prove this.

Any idea. Thanks

Eklavya
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  • Isn't there a theorem which says that every bounded infinite set has a limit point? – bof Jul 04 '19 at 11:29
  • Compare https://math.stackexchange.com/q/962314/42969 – that is about poles, but the same arguments apply to arbitrary types of singularities. – Martin R Jul 04 '19 at 11:34

1 Answers1

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This has nothing to do with Complex Analysis. Any uncountable set in an Euclidean space has a limit point. This is because the points in the set at distance at most $n$ from the origin must be an infinite set for some $n$; any bounded infinite set has a limit point.

Kavi Rama Murthy
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