Advertisement

Multifunctions: the Rudiments

  • Gerald Beer
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 268)

Abstract

If f is a function from a set Y to a set X,then for each xX there may be several points of Y sent by f to x. Thus the inverse assignment x → {y ∈ Y: f(y) = x} is naturally multi-valued, and unless f is onto, some of the values of the inverse are empty. Only when f is a bijection will this assignment be a single-valued function in the usual sense. In this chapter we present the elements of the theory of functions that assign to points of a given set X subsets of a second set Y. Such functions are called set-valued functions or multifunctions. There are a number of set-valued functions that naturally arise in Banach space geometry, some of which we introduce here.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  • Gerald Beer
    • 1
  1. 1.Department of Mathematics and Computer ScienceCalifornia State UniversityLos AngelesUSA

Personalised recommendations