Times: 2026 Mar 11 from 04:55PM to 05:15PM (Central Time (US & Canada))
Abstract:
A fan is an arcwise-connected continuum that is hereditarily unicoherent and has exactly one ramification point. Many known examples of fans have been constructed as one-dimensional continua that are unions of arcs intersecting in exactly one point. In 1954, Borsuk proved that every fan is a one-dimensional continuum that can be expressed as a union of arcs intersecting in exactly one point. However, it is still unknown whether this property characterizes fans. In this talk, I will show under which additional assumptions every such union of arcs is indeed a fan. This is joint work with Iztok Banič, Alejandro Illanes, Ivan Jelić, Judy Kennedy, and Van Nall.