  For a process U(t,s) acting on a one-parameter family of normed spaces, we
present a notion of time-dependent attractor based only on the minimality with
respect to the pullback attraction property. Such an attractor is shown to be
invariant whenever the process is T-closed for some T>0, a much weaker property
than continuity (defined in the text). As a byproduct, we generalize the recent
theory of attractors in time-dependent spaces developed in [10]. Finally, we
exploit the new framework to study the longterm behavior of wave equations with
time-dependent speed of propagation.
