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Spaces of Continuous Functions / by G.L.M. Groenewegen, A.C.M. van Rooij
(Atlantis Studies in Mathematics. ISSN:22151885 ; 4)
版 | 1st ed. 2016. |
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出版者 | Paris : Atlantis Press : Imprint: Atlantis Press |
出版年 | 2016 |
大きさ | IX, 173 p. 23 illus : online resource |
著者標目 | *Groenewegen, G.L.M author van Rooij, A.C.M author SpringerLink (Online service) |
件 名 | LCSH:Functional analysis LCSH:Measure theory FREE:Functional Analysis FREE:Measure and Integration |
一般注記 | 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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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9789462392014 |
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電子リソース |
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EB00206470 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA319-329.9 DC23:515.7 |
書誌ID | 4000116288 |
ISBN | 9789462392014 |
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※2017年9月4日以降