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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.05931 |
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| _version_ | 1866909985232912384 |
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| author | Izzo, Alexander J. |
| author_facet | Izzo, Alexander J. |
| contents | We prove that if E a subset of an n-dimensional manifold, then every continuous R^n-valued map on E that is zero-free on the interior of E can be approximated in the fine topology, and hence, in particular, in the uniform topology, by a continuous R^n-valued map that is zero-free on all of E. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_05931 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximation by zero-free continuous maps Izzo, Alexander J. General Topology We prove that if E a subset of an n-dimensional manifold, then every continuous R^n-valued map on E that is zero-free on the interior of E can be approximated in the fine topology, and hence, in particular, in the uniform topology, by a continuous R^n-valued map that is zero-free on all of E. |
| title | Approximation by zero-free continuous maps |
| topic | General Topology |
| url | https://arxiv.org/abs/2508.05931 |