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Anixx- The reasons for closing were not chosen by us, so for many questions there's no very good choice. If you prefer, I can go back and switch the reason to "not a real question" or "off-topic."
As for why it was closed, you left out so many details that it was completely unanswerable. You hadn't specified a space of functions to use when the question was closed and if you really mean "any function of complex variable" then you have to specify which axioms of set theory you want to use (I have no idea what " I would like to see a counterexample which is impossible with axiom of choice" is supposed to mean. That you don't want counterexamples which require the axiom of choice?). Not to mention that if you want to allow non-differentiable functions you can't use derivative as a linear map, so the question wasn't even internally consistent.
Yes. That tone is surely going to help.
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