
Spaces of Continuous Functions
Atlantis Press (Zeger Karssen)
1st Edition
Published on 27. June 2016
Book
Hardback
IX, 173 pages
978-94-6239-200-7 (ISBN)
Description
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.
Reviews / Votes
"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)More details
Series
Edition
1st ed. 2016
Language
English
Place of publication
Paris
Netherlands
Target group
Professional and scholarly
Illustrations
23 s/w Abbildungen
IX, 173 p. 23 illus.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 16 mm
Weight
448 gr
ISBN-13
978-94-6239-200-7 (9789462392007)
DOI
10.2991/978-94-6239-201-4
Schweitzer Classification
Other editions
Additional editions

G.L.M. Groenewegen | A.C.M. van Rooij
Spaces of Continuous Functions
E-Book
06/2016
1st Edition
Atlantis Press
€82.38
Available for download
Content
Topological Preliminaries.- Metrizable Compact Spaces.- The Stone-Weierstrass Theorem.- Weak Topologies. The Alaoglu Theorem.- Riesz Spaces.- Yosida's Representation Theorem.- The Stone-Cech compactification.- Evaluations.- C(X) determines X.- The Riesz Representation Theorem.- Banach Algebras.- Other Scalars.