Improving Cauchy's Theorem in Constructive Analysis

Douglas S. Bridges

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arXiv · 2410.11058

Improving Cauchy's Theorem in Constructive Analysis

Douglas S. Bridges

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Abstract

In his constructive development of complex analysis, Errett Bishop used restrictive notions of homotopy and simple connectedness. Working in Bishop-style constructive mathematics, we prove Cauchy's integral theorem using the standard notions of such properties. In consequence, Bishop's theorems in Chapters 5 of [1, 2] hold under our more normal, less restrictive, definitions.

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Douglas S. Bridges. 2024-10-14. Improving Cauchy's Theorem in Constructive Analysis. https://arxiv.org/abs/2410.11058

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