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Atlantis Studies in Mathematics

Spaces of Continuous Functions

Authors: Groenewegen, G.L.M., van Rooij, A.C.M.

  • The book contains many exercises. Some are merely illustrations of the theory, others lead to results used in the text. Solutions to the latter and hints for some of the former are to be found at the back of the book
    The book considers various disciplines within functional analysis, highlighting connections between, e.g. ordering and multiplication, or Banach algebras and Boolean rings
    The book has a chapter on spaces of functions with values in other fields that the real or complex numbers
    Every chapter as an "Extra" of either historical or mathematical character
    Little knowledge is assumed. There are appendices for the basics of normed vector spaces and lattice theory

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-94-6239-201-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA
  • ISBN 978-94-6239-200-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

Table of contents (12 chapters)

  • Topological Preliminaries

    Groenewegen, G. L. M. (et al.)

    Pages 1-13

  • Metrizable Compact Spaces

    Groenewegen, G. L. M. (et al.)

    Pages 14-21

  • The Stone-Weierstrass Theorem

    Groenewegen, G. L. M. (et al.)

    Pages 22-28

  • Weak Topologies. The Alaoglu Theorem

    Groenewegen, G. L. M. (et al.)

    Pages 29-40

  • Riesz Spaces

    Groenewegen, G. L. M. (et al.)

    Pages 41-57

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-94-6239-201-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA
  • ISBN 978-94-6239-200-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Spaces of Continuous Functions
Authors
Series Title
Atlantis Studies in Mathematics
Series Volume
4
Copyright
2016
Publisher
Atlantis Press
Copyright Holder
Atlantis Press and the author(s)
eBook ISBN
978-94-6239-201-4
DOI
10.2991/978-94-6239-201-4
Hardcover ISBN
978-94-6239-200-7
Series ISSN
1875-7634
Edition Number
1
Number of Pages
IX, 173
Number of Illustrations and Tables
23 b/w illustrations
Topics