English

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}
}
R2 v1 2026-06-28T19:21:37.810Z