Let Ω1 = {z ∈ ℂ : |z| < 1} and Ω2 = ℂ. If f : Ω2 → Ω1 is holomorphic in ℂ then 

1
f(z) is not entire 
2
f(z) is entire 
3
f(z) is not constant
4
f(z) is unbounded
5
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