Improving Cauchy's Theorem in Constructive Analysis
Logic
2024-10-16 v1
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.
Keywords
Cite
@article{arxiv.2410.11058,
title = {Improving Cauchy's Theorem in Constructive Analysis},
author = {Douglas S. Bridges},
journal= {arXiv preprint arXiv:2410.11058},
year = {2024}
}