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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 )
Product Description
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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Most Helpful Customer Reviews
10 of 10 people found the following review helpful
Format:Paperback
Having scouted the shelves at the Nottingham University library, this was the only text I found which gave an introduction into both Metric and Topological Spaces without the prerequisite for deep previous knowledge. The book starts with a recap of some results from real analysis and develops these comprehensively by first looking at properties of Metric spaces and then the more general topological space scenario. It's a very self contained text with good use of examples and counterexamples to assist learning.
5 of 5 people found the following review helpful
Format:Paperback
I have yet to reach a conclusion on just how good this text is but I do have a word of caution to pass on. Like many maths (and other subjects) this book has loads of questions, which is an excellent way of coming to terms with the material. But unfortunately you cannot get the answers to these questions. This is a problem because (a) it would be nice to know if you are right, and (b) if you are really stuck then you can look at the answer.
The publisher and author's view is that only lecturers at approved institutions, who are using this book as a course text may have the solutions. If you are someone who is trying to master this material alone or you have purchased this book to aid with the coursework you have been given then, I am afraid you are out of luck. You may NOT have access to the answers.
If I had known this then I may not have purchased this book. But to be fair it does tell you this in the preface to the current edition.
The publisher and author's view is that only lecturers at approved institutions, who are using this book as a course text may have the solutions. If you are someone who is trying to master this material alone or you have purchased this book to aid with the coursework you have been given then, I am afraid you are out of luck. You may NOT have access to the answers.
If I had known this then I may not have purchased this book. But to be fair it does tell you this in the preface to the current edition.
5 of 5 people found the following review helpful
Format:Paperback
This is the book that was used in the (now defunct) M435 Topology course at the Open University. Thus I came to know and love this book.
I've taken a look at a few topology texts and they're all more or less difficult to get to grips with. This one is the most accessible of those.
If you need to understand topology for any reason, or you're studying it and it's not on your list of course works, then get it.
I've taken a look at a few topology texts and they're all more or less difficult to get to grips with. This one is the most accessible of those.
If you need to understand topology for any reason, or you're studying it and it's not on your list of course works, then get it.
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Most Recent Customer Reviews
Excellent & enjoyable introduction
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. Read more
Published 17 months ago by Warwick/IC Maths graduate
Excellent Undergraduate Text
This is quite possibly my favourite mathematical textbook. Used in our first year for Oxford undergraduate maths (the earlier edition; and some years ago), I found the book to be... Read more
Published on 25 Nov 2009 by pecanpie557
Good basic introduction to point set topology
I learnt my basic topology from the first edition of this book. Unless you plan to specialise in Topology or a closely related field then this is pretty much all you are going to... Read more
Published on 8 Aug 2009 by Danny of Arabia
Clear and easy to follow
This is an excellent introduction to basic analytic topology and metric spaces. The fundamental concepts are clearly presented and the theory is developed so that it is easy to... Read more
Published on 30 April 2007 by Mr. M. I. Zakiuddin
Clear and rigorous exposition of elementary material.
Complements nicely the metric and topological spaces course lectured in the first year at Cambridge and develops compactness in the proper manner and finishes cleanly with the... Read more
Published on 20 Dec 2006 by J. Oumamar
A comprehenisve book that is easy to read
This is a great book for students taking credits in metric and topological spaces, for example the G13MTS course at Nottingham. Read more
Published on 1 Feb 2001
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