Advertisement

© 2016

Spaces of Continuous Functions

Book
  • 8.4k Downloads

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

  1. 1.Faculty of Education - ILSHAN University of Applied SciencesNijmegenThe Netherlands
  2. 2.Faculty of Science - MathematicsRadboud UniversityNijmegenThe Netherlands

Bibliographic information

  • Book Title Spaces of Continuous Functions
  • Authors G.L.M. Groenewegen
    A.C.M. van Rooij
  • Series Title Atlantis Studies in Mathematics
  • Series Abbreviated Title Atlantis Stud.Math.
  • 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 Mathematics and Statistics (R0)
  • Hardcover ISBN 978-94-6239-200-7
  • eBook ISBN 978-94-6239-201-4
  • Series ISSN 1875-7634
  • Series E-ISSN 2215-1885
  • Edition Number 1
  • Number of Pages IX, 173
  • Number of Illustrations 23 b/w illustrations, 0 illustrations in colour
  • Topics Functional Analysis
    Measure and Integration
  • Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking

Reviews

“This book is a good beginning for people interested in the subject as well as students. The book comprises twelve chapters with a good number of interesting exercises which complement and complete the theory. At the end of the book solutions for the most important exercises as well as hints for others are included. Futhermore, every chapter contains an ‘Extra’ section where the authors relate a story about some mathematician related with the chapter … .” (Jesús Rodríguez-López, Mathematical Reviews, April, 2017)