  We study two variations of Bowen's definitions of topological entropy based
on separated and spanning sets which can be applied to the study of
discontinuous semiflows on compact metric spaces. We prove that these
definitions reduce to Bowen's ones in the case of continuous semiflows. As a
second result, we prove that our entropies give a lower bound for the
$\tau$-entropy defined by Alves, Carvalho and V\'asquez (2015). Finally, we
prove that for impulsive semiflows satisfying certain regularity condition,
there exists a continuous semiflow defined on another compact metric space
which is related to the first one by a semiconjugation, and whose topological
entropy equals our extended notion of topological entropy by using separated
sets for the original semiflow.
