one-to-one holomorphic map of $\mathbb{C}$ onto itself must be of the form $az+b$?
10181
Entire one-to-one functions are linear
125814
The function $f(z)=z+\frac{1}{z}$ maps $\Omega$ biholomorphically on the upper plane
18877
$f(z)$ and $\overline{f(\overline{z})}$ simultaneously holomorphic
108156
Algebraic closure of $\mathbb{C}(x)$ is isomorphic to $\mathbb{C}$
31633
Why is every holomorphic bijection of the Riemann sphere a Möbius transformation?
27629
How to prove that $S^{2n+1}/S^1$ is homeomorphic to $\mathbb CP^n$ under a given identification
84114
Does there exist a surjective homomorphism from $(\mathbb R,+)$ to $(\mathbb Q,+)$ ?
53168
Surjective, Injective, Bijective Functions from $\mathbb Z$ to itself
95669
Solutions of $|z| = z^5$ in $\Bbb{C}$?
146455
Compactness of the set of all unitary matrices in $M_2(\mathbb{C})$
142652
When is the product of two quotient maps a quotient map?
41617
If a $C^1$ map $f:\mathbb{R}^{n}\rightarrow\mathbb{R}^{n}$ is expanding ($\|f(x)-f(y)\|\geq\|x-y\|$), which of these must be true?
134199
Holomorphic function mapping a set onto a straight line
117418
Showing that the image of a function is $\mathbb{C}$ if it satisfies a nice functional equation
157296
Homeomorphism between the Unit Disc and Complex Plane
123891
There are finitely many maps on nonnegative integers satisfying $\phi(ab)=\phi(a)+\phi(b)$
158502
Showing $\sin(\bar{z})$ is not analytic at any point of $\mathbb{C}$