Spaces of Continuous Functions
1st Edition
Published on 17. June 2016
IX, 173 pages
978-94-6239-201-4 (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
Other editions
Additional editions
G.L.M. Groenewegen | A.C.M. van Rooij
Spaces of Continuous Functions
Book
06/2016
1st Edition
Atlantis Press (Zeger Karssen)
€82.38
Shipment within 10-15 days
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.
