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Colloquium Mathematicum

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A fixed-point-free map of a tree-like continuum induced by bounded valence maps on trees

Tom 151 / 2018

Colloquium Mathematicum 151 (2018), 305-316 MSC: Primary 54F15; Secondary 54H25. DOI: 10.4064/cm7070-3-2017 Opublikowany online: 12 January 2018

Streszczenie

Towards attaining a better working understanding of fixed points of maps of tree-like continua, Oversteegen and Rogers constructed a tree-like continuum with a fixed-point-free self-map, described explicitly in terms of inverse limits. Specifically, they defined a sequence of trees $T_n$, $n \in \mathbb{N}$ and maps $f_n$ and $g_n$ from $T_{n+1}$ to $T_n$ for each $n$, such that the $g_n$ maps induce a fixed-point-free self-map of the inverse limit space $\varprojlim (T_n,f_n)$.

The complexity of the trees and the valences of the maps in their example all grow exponentially with $n$, making it difficult to visualize and compute with their space and map. We construct another such example, in which the maps $f_n$ and $g_n$ have uniformly bounded valence, and the trees $T_n$ have a simpler structure.

Autorzy

• Rodrigo Hernández-GutiérrezDepartment of Computer Science & Mathematics
Nipissing University
100 College Drive
Box 5002
North Bay, Ontario, Canada, P1B 8L7
e-mail
• L. C. HoehnDepartment of Computer Science & Mathematics
Nipissing University
100 College Drive
Box 5002
North Bay, Ontario, Canada, P1B 8L7
e-mail

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