  In this paper, we introduce topological entropy for dynamical systems
generated by a single local homeomorphism (Deaconu-Renault systems). More
precisely, we generalize Adler, Konheim, and McAndrew's definition of entropy
via covers and Bowen's definition of entropy via separated sets. We propose a
definition of factor map between Deaconu-Renault systems and show that entropy
(via separated sets) always decreases under uniformly continuous factor maps.
Since the variational principle does not hold in the full generality of our
setting, we show that the proposed entropy via covers is a lower bound to the
proposed entropy via separated sets. Finally, we compute entropy for infinite
graphs (and ultragraphs) and compare it with the entropy of infinite graphs
defined by Gurevich.
