Actions for Spaces of Continuous Functions [electronic resource]

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

Author
Groenewegen, G.L.M.
Published
Paris : Atlantis Press : Imprint: Atlantis Press, 2016.
Physical Description
IX, 173 pages 23 illustrations : online resource
Additional Creators
van Rooij, A.C.M. and SpringerLink (Online service)
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Series
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.
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.
Subject(s)
ISBN
9789462392014
Digital File Characteristics
text file PDF
Part Of
Springer eBooks
View MARC record | catkey: 17949171