# Tagged Questions

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### A homeomorphism preserves irreducible components?

Let $f$ a homeomorphism between two Hausdorff topological spaces $X$ and $Y$. Assume that $X$ and $Y$ are reduced analytic spaces. Is true that $f$ takes an irreducible component of $X$ in an ...
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### Boundary of a holomorphic functions

Let $G ⊆ \mathbb{C}$ a bounded open connected set and let $f : \bar{G} → C$ a holomorphic function: Is this true? $$∂f(G) ⊆ f(∂G)$$ What I have is that $f$ is open.
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### Using uniform continuity to decompose a path in the complex plane

I have a homework problem from Conway's Functions of One Complex Variable that I am stuck on. The problem statement is as follows: Let $G$ be an open subset of $\mathbb{C}$ and let $P$ be a polygon ...
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### Natural surjection from complex upper half plane into modular curve

I am considering the natural surjection $\pi : \mathcal{H} \to Y(\Gamma)$ where $\mathcal{H}$ is the complex upper half plane and $Y(\Gamma)$ the modular curve of the congruence subgroup $\Gamma$. ...
I'm stuck with the following part of exercise 1.1.8 in Hubrechts book Complex geometry: Prove that, if $U \subset \mathbb C^n$ is open connected, then $U \setminus Z(f)$, the complement of zero set ...