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

Irving Kaplansky (Author)

Book Description

Publication Date: 1972 | ISBN-10: 111443762X | ISBN-13: 978-1114437623 | Edition: 1st

This book is based on notes from a course on set theory and metric spaces taught by Edwin Spanier, and also incorporates with his permission numerous exercises from those notes. The volume includes an Appendix that helps bridge the gap between metric and topological spaces, a Selected Bibliography, and an Index.

--This text refers to an alternate Hardcover edition.

Editorial Reviews

Review

"This is a book that could profitably be read by many graduate students or by seniors in strong major programs ... has a number of good features. There are many informal comments scattered between the formal development of theorems and these are done in a light and pleasant style. ... There is a complete proof of the equivalence of the axiom of choice, Zorn's Lemma, and well-ordering, as well as a discussion of the use of these concepts. There is also an interesting discussion of the continuum problem ... The presentation of metric spaces before topological spaces ... should be welcomed by most students, since metric spaces are much closer to the ideas of Euclidean spaces with which they are already familiar." ---- Canadian Mathematical Bulletin<br /><br />"Kaplansky has a well-deserved reputation for his expository talents. The selection of topics is excellent." -- --Lance Small, UC San Diego

"Kaplansky has a well-deserved reputation for his expository talents. The selection of topics is excellent." ---- Lance Small, UC San Diego --This text refers to an alternate Hardcover edition.

Product Details

• Hardcover: 140 pages
• Publisher: Allyn and Bacon; 1st edition (1972)
• Language: English
• ISBN-10: 111443762X
• ISBN-13: 978-1114437623
• ASIN: B0006C31DK
• Product Dimensions: 9 x 5.8 x 0.6 inches
• Shipping Weight: 14.4 ounces
• Average Customer Review: 4.7 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #6,455,849 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

7 of 8 people found the following review helpful:

5.0 out of 5 stars Extremely helpful!, February 8, 2001

By 

Jae Brodsky - See all my reviews

This review is from: Set Theory and Metric Spaces (Hardcover)

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!

4 of 4 people found the following review helpful:

4.0 out of 5 stars Book of Rare Beauty, March 4, 2010

By 

Customer (Baltimore) - See all my reviews

Amazon Verified Purchase

This review is from: Set Theory and Metric Spaces (AMS Chelsea Publishing) (Hardcover)

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.

2 of 2 people found the following review helpful:

5.0 out of 5 stars Extremely helpful!, February 8, 2001

By 

Jae Brodsky - See all my reviews

This review is from: Set Theory and Metric Spaces (Hardcover)

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!