 Fixed point theorems, giving conditions for a function on some set to have a fixed point, are known in many different settings: metric spaces (think of the Banach Fixed Point Theorem), ultrametric spaces (which appear in valuation theory), topological spaces, lattices (with applications to computer science). I will present a general fixed point theorem that represents the underlying principle. I will describe applications to various settings. The general theorem has led to new fixed point theorems and to new insights in the case of the topological setting. No special knowledge will be required from the audience.
This is joint work with my wife Katarzyna Kuhlmann.
