Spaces Of Continuous Functions by G.l.m. GroenewegenSpaces Of Continuous Functions by G.l.m. Groenewegen

Spaces Of Continuous Functions

byG.l.m. Groenewegen, A.c.m. Van Rooij

Hardcover | June 27, 2016

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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.
Title:Spaces Of Continuous FunctionsFormat:HardcoverDimensions:173 pages, 23.5 × 15.5 × 0.03 inPublished:June 27, 2016Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9462392005

ISBN - 13:9789462392007


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-Äech compactification.- Evaluations.- C(X) determines X.- The Riesz Representation Theorem.- Banach Algebras.- Other Scalars.