Spaces of continuous functions

• 作者： Groenewegen, G.L.M., author.
• 其他作者：
  • van Rooij, A.C.M., author.
  • SpringerLink (Online service)
• 其他題名：
  • Atlantis studies in mathematics ;
• 出版： Paris : Atlantis Press :Imprint: Atlantis Press
• 叢書名： Atlantis studies in mathematics,volume 4
• 主題： Functions, Continuous. , Mathematics. , Functional Analysis. , Measure and Integration.
• ISBN： 9789462392014 (electronic bk.) 、 9789462392007 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 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.
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• 摘要註: 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.
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