  We investigate some properties of (universal) Banach spaces of real functions
in the context of topological entropy. Among other things, we show that any
subspace of $C([0,1])$ which is isometrically isomorphic to $\ell_1$ contains a
functions with infinite topological entropy. Also, for any $t \in [0, \infty]$,
we construct a (one-dimensional) Banach space in which any nonzero function has
topological entropy equal to $t$.
