INTRODUCTION TO METRIC AND TOPOLOGICAL SPACES SUTHERLAND PDF

Wilson A. Second editions of maths textbooks occupy a strange place in the literary universe. Alternatively, they may allow the presentation of the material to be refreshed to reflect the expectations of a new generation of readers. The Second Edition under review here falls more into the latter category than the former.

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Wilson A. Second editions of maths textbooks occupy a strange place in the literary universe. Alternatively, they may allow the presentation of the material to be refreshed to reflect the expectations of a new generation of readers. The Second Edition under review here falls more into the latter category than the former.

The target audience for this work comprises undergraduates who have completed a course on the analysis of real-valued functions of one variable. This background is used to review concepts like sequences, limits of functions and continuity in a familiar context. Having established this firm foundation the author generalises these concepts to metric spaces, talking about open and closed sets, interiors and boundaries.

The generalisation is taken further to introduce topological spaces, subspaces and product spaces. Connected, compact and quotient spaces are also covered. The final topic is an example of one that has been amplified in this Second Edition. This website includes a small amount of material from the First Edition, the movement of which has, for example, provided space for the additional discussion of quotient spaces.

The website is also used to provide more detail on tangential topics than would have been possible in a footnote. For example, a pathological example is presented to show the importance of including the Hausdorff condition in the general definition of a closed surface.

A significant strength of this text is the large number of well selected exercises. Even a relatively small seven page chapter on Sequential Compactness is followed by seventeen items to challenge the reader. Unlike the First Edition, answers to the exercises are not included in the book, although they are available on a limited access part of the website.

It is clear that the author has considerable experience in communicating the subject matter, adeptly warning his readers of possible pitfalls or potential sources of confusion. The First Edition of this work was highly praised. It is reassuring to note that the Second Edition is equally impressive. The changes that have been made have only served to enhance the book.

Hence, it remains a highly recommended introduction to metric and topological spaces. The views and opinions expressed herein are those of the author and do not necessarily reflect those of the Defence Science and Technology Laboratory.

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An Introduction to Metric and Topological Spaces (Second Edition)

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Introduction to Metric and Topological Spaces

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