| 书目名称 | Metric Spaces | | 副标题 | A Companion to Analy | | 编辑 | Robert Magnus | | 视频video | | | 概述 | Provides a lucid and clear exposition which includes additional motivation and explanation for delicate points.Presents metric spaces as a tool for advanced analysis, topology and related subjects.Inc | | 丛书名称 | Springer Undergraduate Mathematics Series | | 图书封面 |  | | 描述 | This textbook presents the theory of .Metric Spaces. necessary for studying analysis beyond one real variable. Rich in examples, exercises and motivation, it provides a careful and clear exposition at a pace appropriate to the material..The book covers the main topics of metric space theory that the student of analysis is likely to need.Starting with an overview defining the principal examples of metric spaces in analysis (chapter 1), it turns to the basic theory (chapter 2) covering open and closed sets, convergence, completeness and continuity (including a treatment ofcontinuous linear mappings). There is also a brief dive into general topology, showing how metric spaces fit into a wider theory. The following chapter is devoted to proving the completeness of the classical spaces. The text then embarks on a study of spaces with important special properties.Compact spaces, separable spaces, complete spaces and connected spaces each have a chapter devoted to them.A particular feature of the book is the occasional excursion into analysis. Examples include the Mazur–Ulam theorem, Picard’s theorem on existence of solutions to ordinary differential equations, and space filling curves..T | | 出版日期 | Textbook 2022 | | 关键词 | Textbook on Metric Spaces; Compact Space; Separable Space; Complete Metric Space; Connected Space; Sequen | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-030-94946-4 | | isbn_softcover | 978-3-030-94945-7 | | isbn_ebook | 978-3-030-94946-4Series ISSN 1615-2085 Series E-ISSN 2197-4144 | | issn_series | 1615-2085 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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发表于 2025-3-21 18:15:53
