Xiaoxin Fan

Subspaces of interval maps related to the topological entropy

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.