  We study the Bowen topological entropy of generic and irregular points for
certain dynamical systems. We define the topological entropy of noncompact sets
for flows, analogous to Bowen's definition. We show that this entropy coincides
with the Bowen topological entropy of the time-1 map on any set. We also show a
Bowen's inequality for flows; namely, that the metric entropy with respect to
every invariant measure for a continuous flow is an upper bound for the
topological entropy of the set of generic points with respect to the same
measure, and the equality is always true if the measure is ergodic. We propose
a definition of almost specification property for flows and prove that a
continuous flow has the almost specification property if the time-1 map
satisfies this property. Using Bowen's inequality for flows, we show that every
continuous flow with the almost specification property is saturated, extending
a result of Meson and Vericat in [22]. Under the same hypotheses, we extend a
result of Thompson on the entropy of irregular points in [30].
