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OverviewThe abstract concepts of metric spaces are often perceived as difficult. This book offers a unique approach to the subject which gives readers the advantage of a new perspective on ideas familiar from the analysis of a real line. Rather than passing quickly from the definition of a metric to the more abstract concepts of convergence and continuity, the author takes the concrete notion of distance as far as possible, illustrating the text with examples and naturally arising questions. The book provides a thorough exposition of all the standard necessary results of the theory and, in addition, includes selected topics not normally found in introductory books, such as: the Tietze Extension Theorem; the Hausdorff metric and its completeness; and the existence of curves of minimum length. With its many examples, careful illustrations, and full solutions to selected exercises, this book provides a gentle introduction that is ideal for self-study and an excellent preparation for applications. Full Product DetailsAuthor: Mícheál O'SearcoidPublisher: Springer London Ltd Imprint: Springer London Ltd Edition: 2007 ed. Dimensions: Width: 17.80cm , Height: 1.70cm , Length: 25.40cm Weight: 1.260kg ISBN: 9781846283697ISBN 10: 1846283698 Pages: 304 Publication Date: 08 September 2006 Audience: College/higher education , Undergraduate Format: Paperback Publisher's Status: Active Availability: Awaiting stock ![]() The supplier is currently out of stock of this item. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out for you. Table of ContentsMetrics.- Distance.- Boundary.- Open, Closed and Dense Subsets.- Balls.- Convergence.- Bounds.- Continuity.- Uniform Continuity.- Completeness.- Connectedness.- Compactness.- Equivalence.ReviewsFrom the reviews: <p> This book is truly about metric spaces. a ] The book is packed full of material which does not often appear in comparable books. a ] His use of questions to increase understanding and to move on to the next topic are also to be appreciated. a ] this is a great book and suitable a ] for third-and fourth-year under-graduates and beginning graduate students. (Marion Cohen, MathDL, January, 2007) <p> The book is very readable. It includes appendixes on the necessary mathematical logic and set theory, and has a substantial number of exercisesa ] Every concept is demonstrated via a large number of examples, starting with commonplace ones and expanding the readera (TM)s horizon with the more abstruse ones, to give a sense of the scope of the conceptsa ] A useful addition to any library supporting an undergraduate mathematics major. (D. Z. Spicer, CHOICE, March, 2007) Author InformationMícheál Ó Searcóid is author of another, higher-level, SUMS book, Elements of Abstract Analysis, 1-85233-424-X, published November 2001, sales (as of June 2005): 1051 (ROW: 634; US: 417). Tab Content 6Author Website:Countries AvailableAll regions |