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arXiv · 1910.00154

Subspaces of interval maps related to the topological entropy

Xiaoxin Fan·Jian Li·Yini Yang·Zhongqiang Yang
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Abstract

For $a\in [0,+\infty)$, the function space $E_{\geq a}$ ($E_{>a}$; $E_{\leq a}$; $E_{ a}$ are homeomorphic to the Hilbert space $l_2$ and the spaces $E_{\leq a}$ and $E_{<a}$ are contractible. Moreover, the subspaces of $E_{\leq a}$ and $E_{<a}$ consisting of all piecewise monotone maps are homotopy dense in them, respectively.

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Xiaoxin Fan, Jian Li, Yini Yang, Zhongqiang Yang. 2019-09-30. Subspaces of interval maps related to the topological entropy. https://doi.org/10.12775/tmna.2019.065

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