TITLE: what is the singularity at $z=0$
QUESTION [4 upvotes]: Could any one tell me what is the singularity at $z=0$ of $f(z)=\sin \large({1\over \cos({1\over z})})$?
I know that at $z=0$ $\cos ({1\over z})$ got an essential singularity. I am not able to put it rigorously but I think $f$ too have essential singularity at $z=0$
Thank you.

REPLY [2 votes]: The singularity at $z=0$ is not isolated. The usual classification of removable singularities, poles and essential singularitites are almost always reserved for isolated singularities.
{"set_name": "stack_exchange", "score": 4, "question_id": 470358}