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Spaces of Continuous Functions

G.L.M. Groenewegen, A.C.M. van Rooij (Autoren)

Buch | Hardcover

173 Seiten

2016 | 2016 ed.
Atlantis Press (Zeger Karssen) (Verlag)
978-94-6239-200-7 (ISBN)

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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.

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.

“This book is a good beginning for people interested in the subject as well as students. The book comprises twelve chapters with a good number of interesting exercises which complement and complete the theory. At the end of the book solutions for the most important exercises as well as hints for others are included. Futhermore, every chapter contains an ‘Extra’ section where the authors relate a story about some mathematician related with the chapter … .” (Jesús Rodríguez-López, Mathematical Reviews, April, 2017)

Erscheinungsdatum	16.07.2016
Reihe/Serie	Atlantis Studies in Mathematics ; 4
Zusatzinfo	23 Illustrations, black and white; IX, 173 p. 23 illus.
Verlagsort	Paris
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	Compact Hausdorff Spaces • Representation Theorems • Riesz spaces • spaces of continuous functions • Weak Topologies
ISBN-10	94-6239-200-5 / 9462392005
ISBN-13	978-94-6239-200-7 / 9789462392007
Zustand	Neuware