Customer Reviews

Set theory and metric spaces (Allyn and Bacon series in advanced mathematics)

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Kaplansky's Set Theory and Metric Spaces is one of the most helpful math books that I've ever used. Begining with basic set theory and covering such topics as cardinal numbers, countability, the Axiom of Choice, Zorn's Lemma, well ordering, basic properties of metric spaces, completeness, separability, and compactness. Kaplansky's explanations are clear and concise, his examples are illuminating, and the problems are challenging without being far too difficult. As a bonus, this book is quite resonably priced. A must for anyone who is taking a first or second set theory class!

This is an exceptionally good introduction to the core definitions and theorems of naive set theory.That is to say, it is written in an informal style, yet remains adequate for building deeper knowledge later. I found the treatment somewhat idiosyncratic in that it gives some insights about how Kaplansky views sets and some natural proofs of their properties. Note: this last point suggests the following analogy: you're in college and you take two logic classes just because you love logic so much. However, both are taught by different teachers. One teacher simply goes from the text; the other one hands out a set of lecture notes that is very personal and interesting and adds insight to the textbook. Kaplansky's work is this set of lecture notes. It is also rare to find coverage of metric spaces in a work of its kind, which adds to its appeal. This book is brief, but is not intended to pry beyond the bare essentials -- the written style is ideally suited to this end. A pleasure to read! Highly recommended for a first go.

Kaplansky's Set Theory and Metric Spaces is one of the most helpful math books that I've ever used. Begining with basic set theory and covering such topics as cardinal numbers, countability, the Axiom of Choice, Zorn's Lemma, well ordering, basic properties of metric spaces, completeness, separability, and compactness, this book covered all of the main topics in my set theory class. Kaplansky's explanations are clear and concise, his examples are illuminating, and the problems are challenging without being far too difficult. As a bonus, this book is quite resonably priced. A must for anyone who is taking a first or second set theory class!