• Charalambos D. Aliprantis
  • Kim C. Border


A correspondence is a set-valued function. That is, a correspondence associates to each point in one set a set of points in another set. As such, it can be viewed simply as a subset of the Cartesian product of the two sets. It may seem a bit silly to dedicate two chapters to such a topic, but correspondences arise naturally in many applications. For instance, the budget correspondence in economic theory associates the set of affordable consumption bundles to each price-income combination; the excess demand correspondence is a useful tool in studying economic equilibria; and the best-reply correspondence is the key to analyzing noncooperative games. The theory of “differential inclusions” deals with set-valued differential equations and plays an important role in control theory.


Topological Space Open Neighborhood Topological Vector Space Compact Convex Subset Open Neighborhood Versus 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Charalambos D. Aliprantis
    • 1
  • Kim C. Border
    • 2
  1. 1.Department of EconomicsPurdue UniversityWest LafayetteUSA
  2. 2.Division of the Humanities and Social Sciences 228-77California Institute of TechnologyPasadenaUSA

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