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.
- ISBN13 9789462392007
- Publish Date 27 June 2016
- Publish Status Active
- Publish Country NL
- Imprint Atlantis Press (Zeger Karssen)
- Edition 1st ed. 2016
- Format Hardcover
- Pages 173
- Language English