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Unions of arcs which are fans

Goran Erceg <gorerc@pmfst.hr>, University of Split

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.

Scheduled for: 2026-03-11 04:55 PM: Continua Session #2.4 in Heritage Hall Building 106

Icon: video Webinar

Status: Accepted

Collection: Continuum Theory

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