Stetige Maximierung auf stetigen Urbildern

Conference paper
Part of the Proceedings in Operations Research book series (ORP, volume 1973)


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 2Y, which is given by the Hausdorffmetric on 2Y, is derived by maximization of continuous functions on Y.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Kelley, R.: General Topology. Princeton 1955Google Scholar
  2. [2]
    Kuratowski: Some Problems Concerning Semi-Continuous Set-Valued Mappings. in: Fleischmann (Ed.): Set-Valued Mappings, Selections and Topological Properties of 2X, Berlin 1970Google Scholar
  3. [3]
    Michael: Topologies on Spaces of Subsets, Trans. Amer. Math. Soc. 71 (1951), 152–182CrossRefGoogle Scholar
  4. [4]
    Nikaido: Convex Structures and Economic Theory, London 1968Google Scholar
  5. [5]
    Hildenbrand: Über stetige Korrespondenzen, Operations Research-Verfahren 111(1967)Google Scholar

Copyright information

© Physica-Verlag, Rudolf Liebing KG, Würzburg 1974

Authors and Affiliations

  1. 1.KarlsruheDeutschland

Personalised recommendations