The theory of functions of one complex variable with an emphasis on the theory of complex analytic (or holomorphic) functions of one complex variable. Typical topics include: Cauchy's integral formula, singularities, poles, meromorphic functions, Laurent and Taylor series, maximum modulus principle, ...

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Show that there is no analytic bijection from the unit disc to $\mathbb{C}$

Show that there is no analytic bijection from the unit disc to $\mathbb{C}$. I am quite unsure how to proceed here. I know for a fact that there is no analytic function from $\mathbb{C}$ to the open ...