  We generalize the definition of topological entropy given by Adler, Konheim,
and McAndrew (AKM) for piecewise continuous self-maps defined on a compact
interval (pc-maps). For this notion of entropy, we prove that the properties of
the AKM-entropy in the compact-continuous setting get naturally extended,
including that it can be estimated using Bowen's formula disregarding the
metric used to compute it. Additionally, for piecewise strictly monotonic
pc-maps, we prove that the Misiurewicz-Szlenk formula based on the asymptotic
behavior of the number of monotony pieces for iterations of the map coincides
with our notion of topological entropy. In this way, we unify the notions of
entropy commonly used for piecewise continuous interval maps, proving that they
all coincide when the space is compact.
