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.

Product Details

• Amazon Sales Rank: #34545 in Books
• Published on: 2009-06-18
• Original language: English
• Number of items: 1
• Binding: Paperback
• 224 pages

Customer Reviews

Extremely comprehensive self contained text
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.

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 follow; but the book is also concise and compact (not topologically, I think!!).

I doubt that you could find a better starting place if you want to learn about metric spaces or basic analytic topology.

Excellent course book
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.