Homeomorphisms of composants of Knaster continua
Volume 171 / 2002
Fundamenta Mathematicae 171 (2002), 267-278
MSC: 37B10, 37B45.
DOI: 10.4064/fm171-3-6
Abstract
The Knaster continuum $K_p$ is defined as the inverse limit of the $p$th degree tent map. On every composant of the Knaster continuum we introduce an order and we consider some special points of the composant. These are used to describe the structure of the composants. We then prove that, for any integer $p \ge 2$, all composants of $K_p$ having no endpoints are homeomorphic. This generalizes Bandt's result which concerns the case $p=2$.
