Homeomorphisms of composants of Knaster continua

Volume 171 / 2002

Sonja Štimac Fundamenta Mathematicae 171 (2002), 267-278 MSC: 37B10, 37B45. DOI: 10.4064/fm171-3-6


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 $p=2$.


  • Sonja ŠtimacFaculty of Economics
    University of Zagreb
    Kennedyev trg 6
    10000 Zagreb, Croatia

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