Spaces of Continuous Functions

G.L.M. Groenewegen, A.C.M. van Rooij

ISBN 10: 9462392005 / ISBN 13: 9789462392007

Published by Atlantis Press (Zeger Karssen), NL, 2016

About this Item

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.

Seller Inventory # LU-9789462392007

Bibliographic Details

• Title: Spaces of Continuous Functions
• Publisher: Atlantis Press (Zeger Karssen), NL
• Publication Date: 2016
• Language: English
• ISBN 10: 9462392005
• ISBN 13: 9789462392007
• Binding: Hardback
• Edition: 2016 ed.
• Condition: New

About this title

Synopsis

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.