  For $a\in [0,+\infty)$, the function space $E_{\geq a}$ ($E_{>a}$; $E_{\leq
a}$; $E_{<a}$) of all continuous maps from $[0,1]$ to itself whose topological
entropies are larger than or equal to $a$ (larger than $a$; smaller than or
equal to $a$; smaller than $a$) with the supremum metric is investigated. It is
shown that the spaces $E_{\geq a}$ and $E_{>a}$ 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.
