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
2026-03-25 04:59:49.1774414789
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 ??
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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.