Topology of Linear Spaces and Convex Sets

  • Katsuro Sakai
Part of the Springer Monographs in Mathematics book series (SMM)


In this chapter, several basic results on topological linear spaces and convex sets are presented. We will characterize finite-dimensionality, metrizability, and normability of topological linear spaces. Among the important results are the Hahn–Banach Extension Theorem, the Separation Theorem, the Closed Graph Theorem, and the Open Mapping Theorem. We will also prove the Michael Selection Theorem, which will be applied in the proof of the Bartle–Graves Theorem.


Linear Space Scalar Multiplication Normed Linear Space Affine Function Neighborhood Basis 
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    E. Michael, A generalization of a theorem on continuous selections. Proc. Am. Math. Soc. 105, 236–243 (1989)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Japan 2013

Authors and Affiliations

  • Katsuro Sakai
    • 1
  1. 1.Department of Mathematics Faculty of EngineeringKanagawa UniversityYokohamaJapan

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