$a$ is a non isolated singularity of $f (z)$

Asked Mar 07 '15 at 15:30

Active Mar 07 '15 at 15:34

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If a point $a$ is a non-isolated singularity of a function $f(z)$ and $|f(z)|$ is bounded in some neighbourhood of $a$ then what kind of singularity of $f(z)$ occurs at $a$?

Removable singularity
Essential singularity
Non removable
Non essential

Thank for answer in advance. ..

edited Mar 07 '15 at 15:34

AMPerrine

3,043

asked Mar 07 '15 at 15:30

khushmeet

Do we assume your function is holomorphic on its domain of definition? – Gregory Grant Mar 07 '15 at 15:33
If we take f is holomorphic in its domain of definition then it is analytic then there is no question regarding singularity. Am I right? – khushmeet Mar 07 '15 at 15:59
It cannot be essential by Big Picard's theorem. – Nitin Uniyal Dec 11 '17 at 14:34

$a$ is a non isolated singularity of $f (z)$

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