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Spaces of continuous functions

Groenewegen, G.L.M.

Spaces of continuous functions

Record Type:	Electronic resources : Monograph/item
Title/Author:	Spaces of continuous functionsby G.L.M. Groenewegen, A.C.M. van Rooij.
Author:	Groenewegen, G.L.M.
other author:	van Rooij, A.C.M.
Published:	Paris :Atlantis Press :2016.
Description:	ix, 173 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Functions, Continuous.
Online resource:	http://dx.doi.org/10.2991/978-94-6239-201-4
ISBN:	9789462392014$q(electronic bk.)

Spaces of continuous functions
Groenewegen, G.L.M.

Spaces of continuous functions[electronic resource] /by G.L.M. Groenewegen, A.C.M. van Rooij. - Paris :Atlantis Press :2016. - ix, 173 p. :ill., digital ;24 cm. - Atlantis studies in mathematics,v.41875-7634 ;. - Atlantis studies in mathematics ;v.1..

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

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.

ISBN: 9789462392014$q(electronic bk.)

Standard No.: 10.2991/978-94-6239-201-4doiSubjects--Topical Terms:

732703
Functions, Continuous.

LC Class. No.: QA331

Dewey Class. No.: 515.222

Spaces of continuous functions
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245 1 0 $a Spaces of continuous functions $h [electronic resource] / $c by G.L.M. Groenewegen, A.C.M. van Rooij.
260 $a Paris : $b Atlantis Press : $b Imprint: Atlantis Press, $c 2016.
300 $a ix, 173 p. : $b ill., digital ; $c 24 cm.
490 1 $a Atlantis studies in mathematics, $x 1875-7634 ; $v v.4
505 0 $a Topological Preliminaries -- Metrizable Compact Spaces -- The Stone-Weierstrass Theorem -- Weak Topologies. The Alaoglu Theorem -- Riesz Spaces -- Yosida's Representation Theorem -- The Stone-Cech compactification -- Evaluations -- C(X) determines X -- The Riesz Representation Theorem -- Banach Algebras -- Other Scalars.
520 $a 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.
650 0 $a Functions, Continuous. $3 732703
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Functional Analysis. $3 274845
650 2 4 $a Measure and Integration. $3 273777
700 1 $a van Rooij, A.C.M. $3 750333
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830 0 $a Atlantis studies in mathematics ; $v v.1. $3 544949
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950 $a Mathematics and Statistics (Springer-11649)