Normed Linear Spaces

  • Mahlon M. Day
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 21)


Each of the function spaces mentioned in the introduction of th 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: ∥ x - y ∥ ≦ ε} where ε > 0.


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 1973

Authors and Affiliations

  • Mahlon M. Day
    • 1
  1. 1.University of IllinoisUrbanaUSA

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