A note on the Conley attractors of lower semicontinuous multifunctions

We discuss Conley-type approach to attractive sets for lower semicontinuous multifunctions. Since every iterated function system induces a Barnsley-Hutchinson multifunction which is l.s.c. in such a case it is much more natural to consider a multifunctions of that type then closed relations on compact spaces earlier considered by some authors. We use topological (Kuratowski's) limit instead of commonly used Hausdorff metric.