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Stetige Maximierung auf stetigen Urbildern

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

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

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Literatur

  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

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