{"product_id":"metric-spaces-paperback","title":"Metric Spaces - Paperback","description":"\u003cp\u003eby \u003cb\u003eM兤he疝 O'Searcoid\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe 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. 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.\u003c\/p\u003e \u003cp\u003eEach chapter features copious examples and numerous problems with solutions to some of these provided at the back of the book. 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. Attention to detail at this stage is designed to prepare the reader to understand the more abstract ideas with relative ease.\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe abstract concepts of metric ces are often perceived as difficult. This book offers a unique approach to the subject which gives readers the advantage of a new perspective 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. Attention to detail at this stage is designed to prepare the reader to understand the more abstract ideas with relative ease.\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eThe book goes on to provide 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. Other features include: \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cul\u003e \u003cp\u003e \u003c\/p\u003e\n\u003cli\u003eend-of-chapter summaries and numerous exercises to reinforce what has been learnt;\u003c\/li\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e\n\u003cli\u003eextensive cross-referencing to help the reader follow arguments;\u003c\/li\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e\n\u003cli\u003ea Cumulative Reference Chart, showing the dependencies throughout the book on a section-by-section basis as an aid to course design.\u003c\/li\u003e \u003cp\u003e\u003c\/p\u003e\n\u003c\/ul\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eThe book is designed for third- and fourth-year undergraduates and beginning graduates. Readers should have some practical knowledge of differential and integral calculus and have completed a first course in real analysis. 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.\u003c\/p\u003e\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eM兤he疝 ﾓ Searcd 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). \u003c\/p\u003e\u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 304\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.8 x 10 x 6.9 IN\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e September 08, 2006\u003c\/div\u003e","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":42704842981439,"sku":"9781846283697","price":87.46,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0105\/8226\/1823\/files\/3bc99247434df17df15f0c3b72d25d66.webp?v=1765034747","url":"https:\/\/dhlswag.com\/products\/metric-spaces-paperback","provider":"BBB","version":"1.0","type":"link"}