Fixed set theory for closed correspondences with applications to self-similarity and games. (Q1427924)

The author sketches a general fixed set theory for set-valued maps. It is observed that the existence of a fixed point implies the existence of a nonempty fixed set. If the correspondence is closed, then it is guaranteed to possess a minimal and a largest nonempty closed fixed set. The author also provides sufficient conditions for the fixed sets of the terms of a uniformly convergent sequence of closed self-correspondences on a metric space converge to a fixed set of the limit correspondence. Some applications to game theory are also given.