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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.14934 |
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| _version_ | 1866915680913195008 |
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| author | Adams, Henry Frick, Florian |
| author_facet | Adams, Henry Frick, Florian |
| contents | Brouwer's fixed point theorem states that any continuous function from a closed $n$-dimensional ball to itself has a fixed point. In 1961, Klee showed that if such a function has discontinuities that are bounded, then it has a point that is close to being fixed. We improve upon Klee's results in any finite-dimensional Euclidean space, and prove that our bounds are the best possible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14934 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An optimal Brouwer's fixed point theorem for discontinuous functions Adams, Henry Frick, Florian Metric Geometry Brouwer's fixed point theorem states that any continuous function from a closed $n$-dimensional ball to itself has a fixed point. In 1961, Klee showed that if such a function has discontinuities that are bounded, then it has a point that is close to being fixed. We improve upon Klee's results in any finite-dimensional Euclidean space, and prove that our bounds are the best possible. |
| title | An optimal Brouwer's fixed point theorem for discontinuous functions |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2512.14934 |