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Spaces of continuous functions

Groenewegen, G.L.M.

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Spaces of continuous functions

Record Type:	Electronic resources : Monograph/item
Title/Author:	Spaces of continuous functions/ by 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.
[NT 15003449]:	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.
Contained By:	Springer eBooks
Subject:	Functions, Continuous. -
Online resource:	http://dx.doi.org/10.2991/978-94-6239-201-4
ISBN:	9789462392014

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.3..

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

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

706159
Functions, Continuous.

LC Class. No.: QA331

Dewey Class. No.: 515.222

Spaces of continuous functions
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100 1 $a Groenewegen, G.L.M. $3 2200306
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 706159
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Functional Analysis. $3 893943
650 2 4 $a Measure and Integration. $3 891263
700 1 $a van Rooij, A.C.M. $3 2200307
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Atlantis studies in mathematics ; $v v.3. $3 1568038
856 4 0 $u http://dx.doi.org/10.2991/978-94-6239-201-4
950 $a Mathematics and Statistics (Springer-11649)