Stetige Maximierung auf stetigen Urbildern

Abstract

Let be X, Y, Z topological spaces, A⊆Z.,Φ a mapping from X×Y to Z and g a real function on Y. Then the question is discussed, under which conditions the real function x → max{g(y): Φ(x,y)εA} on X is continuous. A characterisation of the topology on 2^Y, which is given by the Hausdorffmetric on 2^Y, is derived by maximization of continuous functions on Y.