A generic view on the theorems of Brouwer and Schauder (Q1320995)

Let \(K\) be a convex compact subset of a Banach space. The author studies the problem of determining the ``size'' of the fixed point set \(\text{Fix}(f)\) of a ``generic'' continuous map \(f: K\to K\). For example, it is shown that ``most'' maps \(f\) (i.e. all except those in a set of first Baire category), the set \(\text{Fix}(f)\) is homeomorphic to the Cantor set (and hence uncountable).