Math 135 Fall 2024 092524 Open Mapping Theorem; Deformation Theorem
Автор: Winston Ou
Загружено: 2025-02-17
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Описание: (Consequence of Rouche's theorem:) Open Mapping Theorem. Corollaries: Maximum Modulus Principle (two versions). Definition of homotopic curves. Deformation Theorem: integrals of holomorphic functions on homotopic curves are equal. Remark (in reply to student question): there is a theorem (apparently in Bott and Tu's book) that states that the continuous homotopy classes are the same as the smooth homotopy classes. But it doesn't seem to be spelled out in any detail.
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