Introduction to Metric and Topological Spaces [Paperback]

William A. Sutherland (Author)

Book Description

Publication Date: November 13, 1975 | ISBN-10: 0198531613 | ISBN-13: 978-0198531616

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 M�bius 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.

--This text refers to an alternate Paperback edition.

Editorial Reviews

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 --This text refers to an alternate Paperback edition.

About the Author

Wilson A Sutherland was for many years a lecturer in mathematics in the University of Oxford, and a mathematics tutor at New College, Oxford. He has also taught at Massachusetts Institute of Technology and the University of Manchester, and, as a visiting professor, at Yale University and the University of Aberdeen.
--This text refers to an alternate Paperback edition.

Product Details

• Paperback: 196 pages
• Publisher: Oxford University Press, USA (November 13, 1975)
• Language: English
• ISBN-10: 0198531613
• ISBN-13: 978-0198531616
• Product Dimensions: 8.4 x 5.4 x 0.6 inches
• Shipping Weight: 9.1 ounces
• Average Customer Review: 4.7 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #1,766,358 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews

22 of 22 people found the following review helpful:

4.0 out of 5 stars More Rigorous Than Some Introductory Texts, October 31, 2003

By 

Michael Wischmeyer (Houston, Texas) - See all my reviews
(VINE VOICE)    (REAL NAME)   

This review is from: Introduction to Metric and Topological Spaces (Paperback)

I purchased Introduction to Metric and Topological Spaces two years ago. I was unprepared for its rigor. I am not a mathematics major, but I enjoy reading mathematics. My background includes calculus, linear algebra, differential equations, and other applied mathematics, but I have not had a course in real analysis. W. A. Sutherland intended this text as the next step after analysis.

After a brief foray, I retreated, placed Sutherland back on my bookshelf, and attacked some marginally easier introductory texts: Metric Spaces by Victor Bryant, Introduction to Topology by Bert Mendelson, and most recently, several chapters in Introduction to Analysis by Maxwell Rosenlicht. I periodically return to W. A. Sutherland's text to measure my understanding. I am now working on chapter five, Compact Spaces.

I doubt that Introduction to Metric and Topological Spaces would be foreboding to students that are familiar with real analysis. Sutherland understands that the abstractness and generalization can be difficult and shows concern with motivating the student. He repeatedly attempts to illustrate the value of generalization, especially in the study of continuity.

Sutherland often uses a lengthy series of examples of increasing difficulty to illustrate abstract concepts. In his discussion of metric spaces, we begin with Euclidian n-space metrics, and move on to discrete metric spaces, function spaces, and even Hilbert sequence spaces. He introduces open sets and topological spaces in a similar fashion.

The author occasionally suggests that the student might wish to make a geometrical diagram to help clarify some subtle point, but Sutherland includes few geometrical drawings in his text. His focus is clearly on proofs using the axioms of metric spaces and topological spaces.

Sutherland highlights sections that either require more knowledge of abstract algebra, or for other reasons are thought to be more severe.

Despite Sutherland's use of Introduction in the title, I suggest that any reader considering independent study might defer tackling Introduction to Metric and Topological Spaces until after completing a more basic text. Possibly a better title might be A Second Introduction to Metric and Topological Spaces.

9 of 10 people found the following review helpful:

5.0 out of 5 stars A great self-contained text, September 12, 2000

By 

[e-mail] (Aberystwyth, Wales) - See all my reviews

This review is from: Introduction to Metric and Topological Spaces (Paperback)

A lot of books on topology assume some basic knowledge of real analysis, which can throw a lot of readers off. This book starts from the very beginning, and thus is truly a great introduction. Each section has some good exercises, with even a few pointers at the back of the book for the more challenging ones. It starts with topological aspects, and then refers to them in the case of metric spaces (amongst many others), which is a much better approach than most other books, as the reader doesn't take the details of the specific to the general. A great little book, which is a must for most advanced maths Analysis courses.

9 of 10 people found the following review helpful:

5.0 out of 5 stars An excellent, concise book on topology and metric spaces., September 14, 2000

By 

Todd Ebert (Long Beach California) - See all my reviews

This review is from: Introduction to Metric and Topological Spaces (Paperback)

I enjoyed reading this book because of its clarity, conciseness, and nice way of relating topological and metric spaces. This book is ideal for the student who is learning about these subjects for the first time, whether or not they intend to do more advanced work on the subject. The reader who wants to go on and learn about more advanced topics, should consult Munkres's book.