Spaces of Continuous Functions

  • G.L.M. Groenewegen
  • A.C.M. van Rooij
Book

Part of the Atlantis Studies in Mathematics book series (ATLANTISSM, volume 4)

Table of contents

  1. Front Matter
    Pages i-ix
  2. G. L. M. Groenewegen, A. C. M. van Rooij
    Pages 1-13
  3. G. L. M. Groenewegen, A. C. M. van Rooij
    Pages 14-21
  4. G. L. M. Groenewegen, A. C. M. van Rooij
    Pages 22-28
  5. G. L. M. Groenewegen, A. C. M. van Rooij
    Pages 29-40
  6. G. L. M. Groenewegen, A. C. M. van Rooij
    Pages 41-57
  7. G. L. M. Groenewegen, A. C. M. van Rooij
    Pages 58-67
  8. G. L. M. Groenewegen, A. C. M. van Rooij
    Pages 68-76
  9. G. L. M. Groenewegen, A. C. M. van Rooij
    Pages 77-91
  10. G. L. M. Groenewegen, A. C. M. van Rooij
    Pages 92-102
  11. G. L. M. Groenewegen, A. C. M. van Rooij
    Pages 103-124
  12. G. L. M. Groenewegen, A. C. M. van Rooij
    Pages 125-132
  13. G. L. M. Groenewegen, A. C. M. van Rooij
    Pages 133-148
  14. Back Matter
    Pages 149-173

About this book

Introduction

The space C(X) of all continuous functions on a compact space X carries the structure of a normed vector space, an algebra and a lattice. On the one hand we study the relations between these structures and the topology of X, on the other hand we discuss a number of classical results according to which an algebra or a vector lattice can be represented as a C(X). Various applications of these theorems are given.
Some attention is devoted to related theorems, e.g. the Stone Theorem for Boolean algebras and the Riesz Representation Theorem.
The book is functional analytic in character. It does not presuppose much knowledge of functional analysis; it contains introductions into subjects such as the weak topology, vector lattices and (some) integration theory.

Keywords

Spaces of Continuous Functions Compact Hausdorff Spaces Riesz Spaces Representation Theorems Weak Topologies

Authors and affiliations

  • G.L.M. Groenewegen
    • 1
  • A.C.M. van Rooij
    • 2
  1. 1.Faculty of Education - ILSHAN University of Applied SciencesNijmegenThe Netherlands
  2. 2.Faculty of Science - MathematicsRadboud UniversityNijmegenThe Netherlands

Bibliographic information

  • DOI https://doi.org/10.2991/978-94-6239-201-4
  • Copyright Information Atlantis Press and the author(s) 2016
  • Publisher Name Atlantis Press, Paris
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-94-6239-200-7
  • Online ISBN 978-94-6239-201-4
  • Series Print ISSN 1875-7634
  • Series Online ISSN 2215-1885
  • About this book