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.
Spaces of Continuous Functions Compact Hausdorff Spaces Riesz Spaces Representation Theorems Weak Topologies
- Book Title Spaces of Continuous Functions
- 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
Measure and Integration
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“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)