國立虎尾科技大學 |

Spaces of Continuous Functions

Record Type:	Language materials, printed : 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.
Description:	IX, 173 p. 23 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Functional analysis. -
Online resource:	https://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. - 1st ed. 2016. - IX, 173 p. 23 illus.online resource. - Atlantis Studies in Mathematics,41875-7634 ;. - Atlantis Studies in Mathematics,6.

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.

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:

527706
Functional analysis.

LC Class. No.: QA319-329.9

Dewey Class. No.: 515.7

Spaces of Continuous Functions
LDR:02436nam a22003975i 4500 001 979256
003 DE-He213
005 20200701165521.0
007 cr nn 008mamaa
008 201211s2016 fr | s |||| 0|eng d
020 $a 9789462392014 $9 978-94-6239-201-4
024 7 $a 10.2991/978-94-6239-201-4 $2 doi
035 $a 978-94-6239-201-4
050 4 $a QA319-329.9
072 7 $a PBKF $2 bicssc
072 7 $a MAT037000 $2 bisacsh
072 7 $a PBKF $2 thema
082 0 4 $a 515.7 $2 23
100 1 $a Groenewegen, G.L.M. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1110676
245 1 0 $a Spaces of Continuous Functions $h [electronic resource] / $c by G.L.M. Groenewegen, A.C.M. van Rooij.
250 $a 1st ed. 2016.
264 1 $a Paris : $b Atlantis Press : $b Imprint: Atlantis Press, $c 2016.
300 $a IX, 173 p. 23 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Atlantis Studies in Mathematics, $x 1875-7634 ; $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-Čech 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 Functional analysis. $3 527706
650 0 $a Measure theory. $3 527848
650 1 4 $a Functional Analysis. $3 672166
650 2 4 $a Measure and Integration. $3 672015
700 1 $a van Rooij, A.C.M. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1110677
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9789462392007
776 0 8 $i Printed edition: $z 9789462392021
830 0 $a Atlantis Studies in Mathematics, $x 1875-7634 ; $v 6 $3 1271463
856 4 0 $u https://doi.org/10.2991/978-94-6239-201-4
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)