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W. A. Sutherland
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Introduction to Metric and Topological Spaces Paperback – 25 June 2009

by Sutherland (Author)
4.4 4.4 out of 5 stars 34 ratings
Edition: 2nd
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One of the ways in which topology has influenced other branches of mathematics in the past few decades is by putting the study of continuity and convergence into a general setting. This new edition of Wilson Sutherland's classic text introduces metric and topological spaces by describing some of that influence. The aim is to move gradually from familiar real analysis to abstract topological spaces, using metric spaces as a bridge between the two. The language of metric and topological spaces is established with continuity as the motivating concept. Several concepts are introduced, first in metric spaces and then repeated for topological spaces, to help convey familiarity. The discussion develops to cover connectedness, compactness and completeness, a trio widely used in the rest of mathematics. Topology also has a more geometric aspect which is familiar in popular expositions of the subject as `rubber-sheet geometry', with pictures of Möbius bands, doughnuts, Klein bottles and the like; this geometric aspect is illustrated by describing some standard surfaces, and it is shown how all this fits into the same story as the more analytic developments. The book is primarily aimed at second- or third-year mathematics students. There are numerous exercises, many of the more challenging ones accompanied by hints, as well as a companion website, with further explanations and examples as well as material supplementary to that in the book.
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  1. ISBN-10
    019956308X
  2. ISBN-13
    978-0199563081
  3. Edition
    2
  4. Publisher
    Oxford University Press UK
  5. Publication date
    25 June 2009
  6. Language
    English
  7. Dimensions
    1.91 x 15.88 x 23.5 cm
  8. Print length
    224 pages
  9. See all details
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Product description

Review

The presentation, description and explanation throughout the seventeen short chapters are excellent, and the text can be described as self-contained, with many suitably chosen examples and exercises ,.. An interesting innovation for the new edition is having a companion web site in which more useful and relevant materials can be found. ― Peter Shiu, The Mathematical Gazette

Review

`Review from previous edition 'This is a well written and to be recommended text... The book contains an excellent collection of exercises together with a guide to help the reader through these problems.'' Bulletin of the IMA `'...a carefully written introduction... a good, informative, well organized book...'' Jahresbericht der Deutschen Mathematiker-Vereinigung

Product details

  • Publisher ‏ : ‎ Oxford University Press UK; 2 edition (25 June 2009)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 224 pages
  • ISBN-10 ‏ : ‎ 019956308X
  • ISBN-13 ‏ : ‎ 978-0199563081
  • Dimensions ‏ : ‎ 1.91 x 15.88 x 23.5 cm
  • Customer Reviews:
    4.4 4.4 out of 5 stars 34 ratings

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W. A. Sutherland

W. A. Sutherland

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4.4 out of 5 stars
4.4 out of 5
34 global ratings

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Ricardo Acuna
5.0 out of 5 stars Treat it like the bible
Reviewed in the United States on 23 February 2020
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It gives a concrete treatment of metrics before delving into point-set topology.
One person found this helpful
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Yury Ushenin
5.0 out of 5 stars \grazie
Reviewed in Italy on 6 July 2019
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\tutto bene
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unknownman
3.0 out of 5 stars ふつう
Reviewed in Japan on 12 August 2023
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初心者向けで読みやすい。この分野に慣れている人には回りくどい説明である。演習の答えや詳しい解説が公式webのpdfから閲覧できる。webサイトに丸投げな印象もある。ときどき誤植がある。ペーパーバックは開きにくいのでブックスタンドがいる。Terence Taoの Analysis 1に似ている。
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Warwick / Imperial College Maths graduate
5.0 out of 5 stars Excellent & enjoyable introduction
Reviewed in the United Kingdom on 13 December 2010
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One of the best introductions to metric and topological spaces there is. Bear in mind that it is an introductory book but for that purpose it is truly excellent. It has a very strong grounding in making sure that clear explanations and meaningful carefully laid out proofs are given throughout the book.

In particular, the notions behind continuity, uniform continuity and compactness are very well explained in the context of metric spaces (and maths in general) and tied together to then easily step off into topological spaces.

It shows you exactly why topological spaces arose in mathematics as very natural generalisations/companions to metric spaces.

You will find that you will turn back to this book many times in order to keep grounded in the clear explanations and illuminating proofs given here when you go much deeper into the subject.

A very solid 2nd year undergraduate pure maths book. Highly recommended @ Warwick University and Imperial College London.
6 people found this helpful
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Johnnie
5.0 out of 5 stars Well written and very easy to follow.
Reviewed in the United Kingdom on 26 June 2018
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This is a great book and will actually get you through a good amount of different university modules (intro analysis, point set topology, general analysis which extends to metric spaces and also the background topology needed for differential\riemannian geometry). The proofs given in the text are very clear and well explained and are often much better than a lecture; it's ideal of self study.
2 people found this helpful
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