Minimal sets on continua with a dense free interval

TL;DR

This paper characterizes the structure of minimal sets on certain continua with dense free intervals, including spaces like the topologist's sine curve, especially when the remainder is connected or a local dendrite.

Contribution

It provides a full topological characterization of minimal sets on continua with dense free intervals, extending understanding to cases with connected or local dendrite remainders.

Findings

Full characterization of minimal sets when the remainder is connected

Complete description of minimal sets on spaces like the topologist's sine curve

Results applicable to continua with local dendrite remainders

Abstract

We study minimal sets on continua $X$ with a dense free interval $J$ and a locally connected remainder. This class of continua includes important spaces such as the topologist's sine curve or the Warsaw circle. In the case when minimal sets on the remainder are known and the remainder is connected, we obtain a full characterization of the topological structure of minimal sets. In particular, a full characterization of minimal sets on $X$ is given in the case when $X\setminus J$ is a local dendrite.