Openness theorem/theorem of territorial loyalty: Revision history

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26 December 2024

  • curprev 22:3622:36, 26 December 2024 imported>Eshaa2024 6,465 bytes +6,465 New resource with "==Statement== Let <math>U \subseteq\mathbb C</math> be a domain, and let <math>f \colon U \to \mathbb C</math> be a holomorphic, non-constant function. Then, <math>f(U)</math> is a domain. ==Proof== According to the theorem of domain preservation, one must show that <math>f(U)</math> is a domain, i.e., the set <math>f(U)</math> *is connected, and *is open. The proof is divided into these two parts. === Proof 1: Connectedness === We show tha..."
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