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Metric and Normed Spaces

  • George Bachman
  • Lawrence Narici
  • Edward Beckenstein
Chapter
  • 1.1k Downloads
Part of the Universitext book series (UTX)

Abstract

It is natural to think about distance between physical objects—people, say, or buildings or stars. In what follows, we explore — notion of “closeness” for such things as functions and sequences. (How far is f (x)= x3 from g(x) =sin x? How far is the sequence (1/n) from (2/n2)?) The way we answer such — question is through the idea of — metric space.In principle, it enables us to talk about the distance between colorsor ideas or songs. When we can measure “distance,” we can take limits or “perform analysis.” Special distance-measuring devices called norms are introduced for vector spaces. The analysis we care most about in this book involves norms. This type of analysis is known as functional analysis because the vector spaces of greatest interest are spaces of functions.

Keywords

Vector Space Normed Space Triangle Inequality Product Space Minkowski Inequality 
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 Science+Business Media New York 2000

Authors and Affiliations

  • George Bachman
    • 1
  • Lawrence Narici
    • 2
  • Edward Beckenstein
    • 3
  1. 1.Emeritus of MathematicsPolytechnic UniversityBrooklynUSA
  2. 2.Department of Mathematics and Computer ScienceSt. John’s UniversityJamaicaUSA
  3. 3.Science DivisionSt. John’s UniversityStaten IslandUSA

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