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Spaces of continuous functions[electronic resource] /

紀錄類型:	書目-電子資源 : Monograph/item
杜威分類號:	515.222
書名/作者:	Spaces of continuous functions/ by G.L.M. Groenewegen, A.C.M. van Rooij.
作者:	Groenewegen, G.L.M.
其他作者:	van Rooij, A.C.M.
出版者:	Paris : : Atlantis Press :, 2016.
面頁冊數:	ix, 173 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Functions, Continuous.
標題:	Mathematics.
標題:	Functional Analysis.
標題:	Measure and Integration.
ISBN:	9789462392014
ISBN:	9789462392007
內容註:	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.
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.2991/978-94-6239-201-4

Spaces of continuous functions[electronic resource] /
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:

636338
Functions, Continuous.

LC Class. No.: QA331

Dewey Class. No.: 515.222

Spaces of continuous functions[electronic resource] /
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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.
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