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Normed Linear Spaces

  • Mahlon M. Day
Part of the Ergebnisse der Mathematik und Ihrer Grenzgebiete book series (MATHE1, volume 21)

Abstract

Each of the function spaces mentioned in the introduction of the preceding chapter has (with one exception, A (D)) a norm ║ ║ [Definition I, 3, 1] which defines the topology of major interest in the space; a neighborhood basis of a point x is the family of sets {y: ║xy║ ≤ ε} where ε > 0.

Keywords

Banach Space Unit Ball Normed Space Normed Linear Space Continuous Linear Operator 
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 Berlin Heidelberg 1958

Authors and Affiliations

  • Mahlon M. Day
    • 1
  1. 1.UrbanaUSA

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