  We generalize the definition of topological entropy due to Adler, Konheim,
and McAndrew \cite{AKM} to set-valued functions from a closed subset $A$ of the
interval to closed subsets of the interval. We view these set-valued functions,
via their graphs, as closed subsets of $[0,1]^{2}$. We show that many of the
topological entropy properties of continuous functions of a compact topological
space to itself hold in our new setting, but not all. We also compute the
topological entropy of some examples, relate the entropy to other dynamical and
topological properties of the examples, and we give an example of a closed
subset $G$ of $[0,1]^2$ that has $0$ entropy but $G\cup \{ (p,q) \},$ where
$(p,q) \in [0,1]^2\setminus G,$ has infinite entropy.
