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arXiv · 2505.03933

Lelek-like Fans: Endpoint-dense Continua Supporting Topologically Mixing Maps

Iztok Banic·Goran Erceg·Ivan Jelic·Judy Kennedy
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Abstract

The Lelek fan is the only smooth fan that has a dense set of end-points. In this paper, we study non-smooth fans with this property; i.e., we construct an uncountable family of pairwise non-homeomorphic such fans. Furthermore, we prove that each of them admits a topologically mixing non-invertible mapping as well as a topologically mixing homeomorphism.

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Iztok Banic, Goran Erceg, Ivan Jelic, Judy Kennedy. 2025-05-06. Lelek-like Fans: Endpoint-dense Continua Supporting Topologically Mixing Maps. https://arxiv.org/abs/2505.03933

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