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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 › Zeros and Mappings

“ℂ and the unit disc are biholomorphic (both are simply connected)” — false

Counterexample: Liouville's theorem

A biholomorphism 𝔻 $\to C$ would invert to a bounded entire function. $C$ is the sole exception in the Riemann mapping theorem.

complexconformal