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Counterexample bank

Part C is won by knowing which tempting claims are false. 148 counterexamples; 85 free. The rest come with the Notes pack.

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#1 · Complex Analysis, Algebra & Topology › Singularities and Residues

“Zeros of a non-constant analytic function can accumulate inside the domain” — false

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complexzeros

#2 · Complex Analysis, Algebra & Topology › Analytic Functions

“Zeros of a non-constant holomorphic function cannot accumulate” — false

Counterexample: sin(1/z) on ℂ∖{0}

Zeros $1/ (nπ)$ accumulate at 0, which lies outside the domain. Inside the domain zeros are always isolated.

complexzeros