On a new proof of the key step in the proof of Brouwer's fixed point theorem
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909496459132928 |
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| author | Krylov, N. V. |
| author_facet | Krylov, N. V. |
| contents | We present a solution of Exercise 1.2.1 of [2] which yields a short new proof of a key step in one of proofs of Brouwer's fixed point theorem, 1910. A few people asked the author about the details of the solution and they might be interesting to a broader audience. Our approach is absolutely different from the ones using algebraic or differential topology or differential calculus and is based on a simple observation which somehow escaped many authors treating this theorem in the past. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_11311 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a new proof of the key step in the proof of Brouwer's fixed point theorem Krylov, N. V. Classical Analysis and ODEs Functional Analysis 47H10 We present a solution of Exercise 1.2.1 of [2] which yields a short new proof of a key step in one of proofs of Brouwer's fixed point theorem, 1910. A few people asked the author about the details of the solution and they might be interesting to a broader audience. Our approach is absolutely different from the ones using algebraic or differential topology or differential calculus and is based on a simple observation which somehow escaped many authors treating this theorem in the past. |
| title | On a new proof of the key step in the proof of Brouwer's fixed point theorem |
| topic | Classical Analysis and ODEs Functional Analysis 47H10 |
| url | https://arxiv.org/abs/2502.11311 |