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Topological and Geometrical Properties of Locally Convex Spaces

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Part of the Grundlehren der mathematischen Wissenschaften book series (GL,volume 159)

Abstract

We continue with the general theory of locally convex spaces. In § 23 the bidual space is introduced, and the question of the semi-reflexivity or reflexivity of a locally convex space is raised. A number of criteria are established, and we examine the connection with other structural properties.

Keywords

  • Extreme Point
  • Unit Ball
  • Convex Space
  • Strong Topology
  • Closed Unit Ball

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© 1983 Springer-Verlag Berlin, Heidelberg

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Köthe, G. (1983). Topological and Geometrical Properties of Locally Convex Spaces. In: Topological Vector Spaces I. Grundlehren der mathematischen Wissenschaften, vol 159. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-64988-2_5

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  • DOI: https://doi.org/10.1007/978-3-642-64988-2_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64990-5

  • Online ISBN: 978-3-642-64988-2

  • eBook Packages: Springer Book Archive