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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2410.11058 |
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| _version_ | 1866910650795556864 |
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| author | Bridges, Douglas S. |
| author_facet | Bridges, Douglas S. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11058 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Improving Cauchy's Theorem in Constructive Analysis Bridges, Douglas S. Logic 03F60 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. |
| title | Improving Cauchy's Theorem in Constructive Analysis |
| topic | Logic 03F60 |
| url | https://arxiv.org/abs/2410.11058 |