Spaces of Continuous Functions

• Main Authors: Groenewegen, G.L.M (Author), van Rooij, A.C.M (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Paris : Atlantis Press : Imprint: Atlantis Press, 2016.
• Series: Atlantis Studies in Mathematics, 4
• Subjects: Mathematics.; Functional analysis.; Measure theory.; Functional Analysis.; Measure and Integration.

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 whi...

Table of Contents:

• Topological Preliminaries
• Metrizable Compact Spaces
• The Stone-Weierstrass Theorem
• Weak Topologies. The Alaoglu Theorem
• Riesz Spaces
• Yosida’s Representation Theorem
• The Stone-Čech compactification
• Evaluations
• C(X) determines X
• The Riesz Representation Theorem
• Banach Algebras
• Other Scalars.