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Homotopy of Closed Curves in the Complex Plane
Автор: Mike, the Mathematician
Загружено: 2025-04-14
Просмотров: 745
Описание:
Given two closed curves in the complex plane, can one be continuously deformed into the other? This is precisely the question addressed by the concept of homotopy. Two closed curves in the complex plane are said to be homotopic if there exists a continuous function from the product of the unit interval and the parameter space into the complex plane that continuously transforms one curve into the other. This notion plays a central role in topology and underlies the more general formulation of Cauchy's Theorem.
#mikedabkowski, #mikethemathematician, #profdabkowski, #complexanalysis, #homotopy
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