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Linear Topological Spaces

  • John L. Kelley
  • Isaac Namioka
  • W. F. DonoghueJr.
  • Kenneth R. Lucas
  • B. J. Pettis
  • Ebbe Thue Poulsen
  • G. Baley Price
  • Wendy Robertson
  • W. R. Scott
  • Kennan T. Smith
Part of the Graduate Texts in Mathematics book series (GTM, volume 36)

Abstract

This chapter is largely preliminary in nature; it consists of a brief review of some of the terminology and the elementary theorems of general topology, an examination of the new concept “linear topological space” in terms of more familiar notions, and a comparison of this new concept with the mathematical objects of which it is an abstraction. After an introductory section on topology, we consider linear topological spaces, subspaces, quotient spaces, product spaces, and linear functions. With the exception of a few simple propositions relating to circled sets, these theorems are specializations of familiar results on topological groups (in other words, little use is made of scalar multiplication).

Keywords

Local Base Pointwise Convergence Neighborhood System Finite Dimensional Subspace Linear Topological Space 
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

© J. L. Kelley and G. B. Price 1963

Authors and Affiliations

  • John L. Kelley
    • 1
  • Isaac Namioka
    • 2
  • W. F. DonoghueJr.
  • Kenneth R. Lucas
  • B. J. Pettis
  • Ebbe Thue Poulsen
  • G. Baley Price
  • Wendy Robertson
  • W. R. Scott
  • Kennan T. Smith
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA
  2. 2.Department of MathematicsUniversity of WashingtonSeattleUSA

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