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Systems of Continuos Functions

  • Volker Runde
  • S Axler
  • K.A. Ribet
Chapter
  • 3.2k Downloads
Part of the Universitext book series (UTX)

Abstract

Topological spaces were introduced in the first place because they are the natural habitat for continuous functions.

Given two topological spaces X and Y , the number of continuous functions from X to Y can vary greatly, depending on the topologies involved: everything is possible from “all functions are continuous” to “only the constants are continuous.” In this chapter, we are interested in continuous functions from topological spaces into R or C. On a metric space, the metric itself easily provides a plentiful supply of such functions. But can anything meaningful be said in the absence of a metric?

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Volker Runde
    • 1
  • S Axler
    • 2
  • K.A. Ribet
    • 3
  1. 1.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada
  2. 2.Mathematics DepartmentSan Francisco State UniversitySan FranciscoUSA
  3. 3.Mathematics DepartmentUniversity of California at BerkeleyBerkeleyCAUSA

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