Spaces of Continuous Functions / by G.L.M. Groenewegen, A.C.M. van Rooij.

Format:

Book

Author/Creator:

Groenewegen, G.L.M., Author.

van Rooij, A.C.M., Author.

Series:

Atlantis Studies in Mathematics, 2215-1885 ; 4

Language:

English

Subjects (All):

Functional analysis.

Measure theory.

Functional Analysis.

Measure and Integration.

Local Subjects:

Functional Analysis.

Measure and Integration.

Physical Description:

1 online resource (IX, 173 p. 23 illus.)

Edition:

1st ed. 2016.

Place of Publication:

Paris : Atlantis Press : Imprint: Atlantis Press, 2016.

Summary:

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.

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.

Notes:

Includes bibliographical references at the end of each chapters and index.

ISBN:

94-6239-201-3