Spaces of Continuous Functions

2016
ISBN: 978-94-6239-200-7
Verlag: Atlantis Press

Buch, Englisch, Band 4, 173 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 4026 g

Reihe: Atlantis Studies in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Rooij, A. C. M. van

Groenewegen, G.L.M.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Vektoranalysis, Physikalische Felder

Inhaltsverzeichnis

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.