Towards the complete classification of fans
Dynamical Systems
2026-04-14 v3
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.
Cite
@article{arxiv.2504.07267,
title = {Towards the complete classification of fans},
author = {Iztok Banič and Goran Erceg and Alejandro Illanes and Ivan Jelić and Judy Kennedy and Van Nall},
journal= {arXiv preprint arXiv:2504.07267},
year = {2026}
}