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＜E-Book＞
Spaces of Continuous Functions / by G.L.M. Groenewegen, A.C.M. van Rooij
(Atlantis Studies in Mathematics. ISSN:22151885 ; 4)

Edition	1st ed. 2016.
Publisher	(Paris : Atlantis Press : Imprint: Atlantis Press)
Year	2016
Size	IX, 173 p. 23 illus : online resource
Authors	*Groenewegen, G.L.M author van Rooij, A.C.M author SpringerLink (Online service)
Subjects	LCSH:Functional analysis LCSH:Measure theory FREE:Functional Analysis FREE:Measure and Integration
Notes	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 HTTP:URL=https://doi.org/10.2991/978-94-6239-201-4

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