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Functions on metric spaces

  • M. H. Protter
  • C. B. MorreyJr.
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

We developed many of the basic properties of metric spaces in Chapter 6. A complete metric space was defined in Chapter 13 and we saw the importance of such spaces in the proof of the fundamental fixed point theorem (Theorem 13.2). This theorem, which has many applications, was used to prove the existence of solutions of differential equations and the Implicit function theorem. We now discuss in more detail functions whose domain is a metric space, and we prove convergence and approximation theorems which are useful throughout analysis.

Keywords

Continuous Function Convex Function Compact Subset Interior Point Cauchy Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag, New York Inc. 1977

Authors and Affiliations

  • M. H. Protter
    • 1
  • C. B. MorreyJr.
    • 1
  1. 1.Department of MathematicsUniversity of California at BerkeleyBerkeleyUSA

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