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Spaces of Continuous Functions

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/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.
面頁冊數:	IX, 173 p. 23 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Functional analysis. -
電子資源:	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
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