Towards the complete classification of fans
Fuente:
arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866913022993235968 |
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| author | Banič, Iztok Erceg, Goran Illanes, Alejandro Jelić, Ivan Kennedy, Judy Nall, Van |
| author_facet | Banič, Iztok Erceg, Goran Illanes, Alejandro Jelić, Ivan Kennedy, Judy Nall, Van |
| contents | A fan is an arcwise-connected continuum, which is hereditarily unicoherent and has exactly one ramification point. Many of the known examples of fans were constructed as 1-dimensional continua that are unions of arcs which intersect in exactly one point. Borsuk proved in 1954 that each fan is a 1-dimensional continuum which is the union of arcs intersecting in exactly one point. But it is not yet known if this property is equivalent to being a fan. In this paper, we show that under two additional assumptions, every such union of arcs is a fan. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07267 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Towards the complete classification of fans Banič, Iztok Erceg, Goran Illanes, Alejandro Jelić, Ivan Kennedy, Judy Nall, Van Dynamical Systems 54F15 A fan is an arcwise-connected continuum, which is hereditarily unicoherent and has exactly one ramification point. Many of the known examples of fans were constructed as 1-dimensional continua that are unions of arcs which intersect in exactly one point. Borsuk proved in 1954 that each fan is a 1-dimensional continuum which is the union of arcs intersecting in exactly one point. But it is not yet known if this property is equivalent to being a fan. In this paper, we show that under two additional assumptions, every such union of arcs is a fan. |
| title | Towards the complete classification of fans |
| topic | Dynamical Systems 54F15 |
| url | https://arxiv.org/abs/2504.07267 |