| 书目名称 | Foundations of Real and Abstract Analysis | | 编辑 | Douglas S. Bridges | | 视频video | | | 概述 | A wide range of material * Clear and concise format * Unique collection of nearly 750 exercises *.Pointers to new branches of the subject | | 丛书名称 | Graduate Texts in Mathematics | | 图书封面 |  | | 描述 | The core of this book, Chapters three through five, presents a course on metric, normed, and Hilbert spaces at the senior/graduate level. The motivation for each of these chapters is the generalisation of a particular attribute of the n Euclidean space R: in Chapter 3, that attribute is distance; in Chapter 4, length; and in Chapter 5, inner product. In addition to the standard topics that, arguably, should form part of the armoury of any graduate student in mathematics, physics, mathematical economics, theoretical statistics,. . . , this part of the book contains many results and exercises that are seldom found in texts on analysis at this level. Examples of the latter are Wong’s Theorem (3.3.12) showing that the Lebesgue covering property is equivalent to the uniform continuity property, and Motzkin’s result (5. 2. 2) that a nonempty closed subset of Euclidean space has the unique closest point property if and only if it is convex. The sad reality today is that, perceiving them as one of the harder parts of their mathematical studies, students contrive to avoid analysis courses at almost any cost, in particular that of their own educational and technical deprivation. Many univers | | 出版日期 | Textbook 1998 | | 关键词 | Hilbert space; calculus; differential equation; functional analysis; mathematical economics; real analysi | | 版次 | 1 | | doi | https://doi.org/10.1007/b97625 | | isbn_softcover | 978-1-4757-7161-9 | | isbn_ebook | 978-0-387-22620-0Series ISSN 0072-5285 Series E-ISSN 2197-5612 | | issn_series | 0072-5285 | | copyright | Springer Science+Business Media New York 1998 |
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发表于 2025-3-21 19:22:19
