An uncountable family of non-smooth fans that admit transitive homeomorphisms
Iztok Banic, Judy Kennedy, Chris Mouron, Van Nall
TL;DR
This paper constructs an uncountable family of non-smooth fans that are pairwise non-homeomorphic yet admit transitive homeomorphisms, expanding the understanding of dynamical properties in topological fans.
Contribution
It introduces a new family of non-smooth fans with transitive homeomorphisms, contrasting previous work focused on smooth fans.
Findings
Uncountably many non-homeomorphic non-smooth fans constructed
All constructed fans admit transitive homeomorphisms
Expands the class of known topological fans with dynamical properties
Abstract
Recently, many examples of smooth fans that admit a transitive homeomorphism have been constructed. For example, a family of uncountably many pairwise non-homeomorphic smooth fans that admit transitive homeomorphisms was constructed. In this paper, we construct a family of uncountably many pairwise non-homeomorphic non-smooth fans that admit transitive homeomorphisms.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Differential Equations and Dynamical Systems · Advanced Topology and Set Theory