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
- 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
- Print ISBN 978-94-6239-200-7
- Online ISBN 978-94-6239-201-4
- Series Print ISSN 1875-7634
- Series Online ISSN 2215-1885
- About this book