| 书目名称 | Elements of Abstract Analysis | | 编辑 | Mícheál Ó Searcóid | | 视频video | | | 概述 | Provides a thorough treatment of the elements of modern analysis including a systematic treatment of the set theory which analysts need to know.Aimed specifically at final year undergraduates, it revi | | 丛书名称 | Springer Undergraduate Mathematics Series | | 图书封面 |  | | 描述 | In nature‘s infinite book ofsecrecy A little I can read. Antony and Cleopatra, l. ii. This is a book about a few elementary concepts of analysis and the mathe matical structures which enfold them. It is more concerned with the interplay amongst these concepts than with their many applications. The book is self-contained; in the first chapter, after acknowledging the fundamental role ofmathematical logic, wepresent seven axioms of Set Theory; everything else is developed from these axioms. It would therefore be true, if misleading, to say that the reader requires no prior knowledge of mathematics. In reality, the reader we have in mind has that level of sophistication achieved in about three years of undergraduate study of mathematics and is already well acquainted with most of the structures discussed-rings, linear spaces, metric spaces, and soon-and with many ofthe principal analytical concepts convergence, connectedness, continuity,compactness and completeness. Indeed, it is only after gaining familiarity with these concepts and their applications that it is possible to appreciate their place within a broad framework of set based mathematics and to consolidate an understanding | | 出版日期 | Textbook 2002 | | 关键词 | calculus; compactness; convergence; functional analysis; metric space | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4471-0179-6 | | isbn_softcover | 978-1-85233-424-6 | | isbn_ebook | 978-1-4471-0179-6Series ISSN 1615-2085 Series E-ISSN 2197-4144 | | issn_series | 1615-2085 | | copyright | Springer-Verlag London 2002 |
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发表于 2025-3-21 18:31:23
