Towards the complete classification of fans

[2504.07267] Towards the complete classification of fans Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Dynamical Systems arXiv:2504.07267 (math) [Submitted on 9 Apr 2025 ( v1 ), last revised 11 Apr 2026 (this version, v3)] Title: Towards the complete classification of fans Authors: Iztok Banič , Goran Erceg , Alejandro Illanes , Ivan Jelić , Judy Kennedy , Van Nall View a PDF of the paper titled Towards the complete classification of fans, by Iztok Bani\v{c} and 5 other authors View PDF HTML (experimental) Abstract: 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. Subjects: Dynamical Systems (math.DS) MSC classes: 54F15 Cite as: arXiv:2504.07267 [math.DS] (or arXiv:2504.07267v3 [math.DS] for this version) https://doi.org/10.48550/arXiv.2504.07267 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ivan Jelić [ view email ] [v1] Wed, 9 Apr 2025 20:45:25 UTC (17,869 KB) [v2] Fri, 27 Mar 2026 10:27:33 UTC (17,865 KB) [v3] Sat, 11 Apr 2026 18:51:57 UTC (17,865 KB) Full-text links: Access Paper: View a PDF of the paper titled Towards the complete classification of fans, by Iztok Bani\v{c} and 5 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.DS < prev | next > new | recent | 2025-04 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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