On a local property of fences and fans
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866912565523644416 |
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| author | Lipham, David S. |
| author_facet | Lipham, David S. |
| contents | Two closely related classes of topological spaces are fences and fans. A fence is a compact metric space whose components are either arcs or singletons. A fan is a continuum formed by joining arcs at a common vertex, in such a way that intersections of subcontinua are always connected. We prove that every fence can be embedded in the plane and that both fences and fans admit a basis consisting of pierced open sets. This resolves a question by Iztok Banič, Goran Erceg, Ivan Jelić, Judy Kennedy, and Van Nall. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03530 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a local property of fences and fans Lipham, David S. General Topology 54F15, 54F45 Two closely related classes of topological spaces are fences and fans. A fence is a compact metric space whose components are either arcs or singletons. A fan is a continuum formed by joining arcs at a common vertex, in such a way that intersections of subcontinua are always connected. We prove that every fence can be embedded in the plane and that both fences and fans admit a basis consisting of pierced open sets. This resolves a question by Iztok Banič, Goran Erceg, Ivan Jelić, Judy Kennedy, and Van Nall. |
| title | On a local property of fences and fans |
| topic | General Topology 54F15, 54F45 |
| url | https://arxiv.org/abs/2508.03530 |