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arXiv · 2504.07267

Towards the complete classification of fans

Iztok Banič·Goran Erceg·Alejandro Illanes·Ivan Jelić·Judy Kennedy·Van Nall
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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.

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Iztok Banič, Goran Erceg, Alejandro Illanes, Ivan Jelić, Judy Kennedy, Van Nall. 2025-04-09. Towards the complete classification of fans. https://arxiv.org/abs/2504.07267

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