Part CCSIR NET December 2023liouville-obstruction

Liouville obstruction

Let $Ω_{1} =$ { $z \in C$ : |z| < 1} and $Ω_{2} = C$ . Which of the following statements are true?

A.There exists a holomorphic surjective map $f : Ω_{1} \to Ω_{2}$ .✓
B.There exists a holomorphic surjective map $f : Ω_{2} \to Ω_{1}$ .
C.There exists a holomorphic injective map $f : Ω_{1} \to Ω_{2}$ .✓
D.There exists a holomorphic injective map $f : Ω_{2} \to Ω_{1}$ .

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests standard counterexample.

See pricing

50 are analysed free — try those first.

The trap it tests

Standard counterexample

There is a canonical object that settles this. Recognising it is the whole question.

Drill statements like this

Liouville obstruction

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