ON THE CONTINUITY OF GLOBAL ATTRACTORS

Let A be a complete metric space, and let {S-lambda(.) : lambda is an element of A} be a parametrised family of semigroups with global attractors A(lambda). We assume that there exists a fixed bounded set D such that A(lambda) subset of D for every lambda is an element of A. By viewing the attractors as the limit as t -> infinity of the sets S-lambda(t) D, we give simple proofs of the equivalence of 'equi-attraction' to continuity (when this convergence is uniform in.) and show that the attractors A. are continuous in. at a residual set of parameters in the sense of Baire Category (when the convergence is only pointwise).