  Using Conley theory we show that local attractors remain (past) attractors
under small non-autonomous perturbations. In particular, the attractors of the
perturbed systems will have positive invariant neighborhoods and converge upper
semicontinuously to the original attractor.
  The result is split into a finite-dimensional part (locally compact) and an
infinite-dimensional part (not necessarily locally compact). The
finite-dimensional part will be applicable to bounded random noise, i.e.
continuous time random dynamical systems on a locally compact metric space
which are uniformly close the unperturbed deterministic system. The "closeness"
will be defined via a (simpler version of) convergence coming from singular
perturbations theory.
