The Open Mapping and Closed Graph Theorems in Topological Vector Spaces

  • Taqdir Husain

Table of contents

  1. Front Matter
    Pages iii-x
  2. Taqdir Husain
    Pages 11-33
  3. Taqdir Husain
    Pages 34-44
  4. Taqdir Husain
    Pages 71-81
  5. Taqdir Husain
    Pages 96-100
  6. Back Matter
    Pages 101-108

About this book

Introduction

THE main purpose of writing this monograph is to give a picture of the progress made in recent years in understanding three of the deepest results of Functional Analysis-namely, the open-mapping and closed­ graph theorems, and the so-called Krein-~mulian theorem. In order to facilitate the reading of this book, some of the important notions and well-known results about topological and vector spaces have been collected in Chapter 1. The proofs of these results are omitted for the reason that they are easily available in any standard book on topology and vector spaces e.g. Bourbaki [2], Keiley [18], or Köthe [22]. The results of Chapter 2 are supposed to be weil known for a study of topological vector spaces as weil. Most of the definitions and notations of Chapter 2 are taken from Bourbaki's books [3] and [4] with some trimming and pruning here and there. Keeping the purpose of this book in mind, the presentation of the material is effected to give a quick resume of the results and the ideas very commonly used in this field, sacrificing the generality of some theorems for which one may consult other books, e.g. [3], [4], and [22]. From Chapter 3 onward, a detailed study of the open-mapping and closed-graph theorems as weil as the Krein-~mulian theorem has been carried out. For the arrangement of the contents of Chapters 3 to 7, see the Historical Notes (Chapter 8).

Keywords

THE Vector space boundary element method field function functional functional analysis graph locally convex space mapping presentation proof theorem topological vector space topology

Authors and affiliations

  • Taqdir Husain
    • 1
  1. 1.McMaster UniversityHamiltonCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-322-96210-2
  • Copyright Information Springer Fachmedien Wiesbaden GmbH 1965
  • Publisher Name Vieweg+Teubner Verlag, Wiesbaden
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-322-96077-1
  • Online ISBN 978-3-322-96210-2
  • About this book