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The Index of a Curve About a Point is Continuous at that Point
Автор: Mike, the Mathematician
Загружено: 2025-04-17
Просмотров: 337
Описание:
We prove that the index of a closed curve about a point in the complex plane is a continuous function of that point. Since the index is always an integer, we see that the index is constant on each component of the complex plane. From this it follows that the index of a curve must be zero on the unbounded component of the curve.
#mikethemathematician, #profdabkowski, #mikedabkowski, #complexanalysis, #indexofacurve
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