Topological Spaces: From Distance to Neighborhood (Undergraduate Texts in Mathematics) [Hardcover]

Gerard Buskes (Author), Arnoud van Rooij (Author)

Book Description

ISBN-10: 0387949941 | ISBN-13: 978-0387949949 | Publication Date: August 15, 1997 | Edition: 1

gentle introduction to the subject, leading the reader to understand the notion of what is important in topology with regard to geometry. Divided into three sections - The line and the plane, Metric spaces and Topological spaces -, the book eases the move into higher levels of abstraction. Students are thereby informally assisted in learning new ideas while remaining on familiar territory. The authors do not assume previous knowledge of axiomatic approach or set theory. Similarly, they have restricted the mathematical vocabulary in the book so as to avoid overwhelming the reader, and the concept of convergence is employed to allow students to focus on a central theme while moving to a natural understanding of the notion of topology. The pace of the book is relaxed with gradual acceleration: the first nine sections form a balanced course in metric spaces for undergraduates while also containing ample material for a two-semester graduate course. Finally, the book illustrates the many connections between topology and other subjects, such as analysis and set theory, via the inclusion of "Extras" at the end of each chapter presenting a brief foray outside topology.

Editorial Reviews

Review

This is a gentle introduction to topological spaces leading the reader to understand the notion of what is important in topology vis-a-vis geometry and analysis. The authors have carefully divided the book into three sections; The line and the plane, Metric spaces and Topological spaces, in order to mitigate the move into higher levels of abstraction. Students are thereby informally assisted in getting aquainted with new ideas while remaining on familiar territory. The authors have also restricted the mathematical vocabulary in the book to avoid overwhelming the reader with the extensive array of technical terms indicating the properties of topological spaces. Additionally, the concept of convergence is employed to allow students to focus on a central theme while moving to a natural understanding of the notion of topology. -- Book Description

Product Details

• Hardcover: 320 pages
• Publisher: Springer; 1 edition (August 15, 1997)
• Language: English
• ISBN-10: 0387949941
• ISBN-13: 978-0387949949
• Product Dimensions: 9.3 x 6.2 x 1 inches
• Shipping Weight: 1.3 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #584,486 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews

17 of 19 people found the following review helpful:

5.0 out of 5 stars I wish all math books were like this..., January 5, 2000

By 

Rob Kosman (Enschede, Netherlands) - See all my reviews

This review is from: Topological Spaces: From Distance to Neighborhood (Undergraduate Texts in Mathematics) (Hardcover)

I'm a graduate student in mathematics and this is one of the few math books I can highly recommend. Topological concepts are made intuitive, so when you get to the formal definitions, they are no surprise, you even expect them. Sometimes it is explained why a 'seemingly obvious solution' doesn't work after all. This really helps you to see WHY things are done the way they are. After reading this book you'll have a good basic understanding of what topology is all about. With this background it should be no problem to tackle more advanced texts on topology.

By the way, I love the 'Extras' in the book. They are little pieces of history or excursions into other parts of mathematics that can be found at the end of each chapter.

8 of 8 people found the following review helpful:

5.0 out of 5 stars Best book ever on topology!, December 9, 1997

By A Customer

This review is from: Topological Spaces: From Distance to Neighborhood (Undergraduate Texts in Mathematics) (Hardcover)

This book is an extremely valuable asset to anyone with enthusiasm for mathematics. Using at first only fundemental calculus, the book carefully draws the reader into the scope of the field. The book contains detailed explanation of all terms used in the axioms and theorms presented. It leaves an unambiguous picture of the developed ideas in the reader's mind. I strongly recommend it, (it even has a neat cover!)

5 of 5 people found the following review helpful:

5.0 out of 5 stars probably the best undergraduate level topology book, June 25, 2003

By 

UNPINGCO (Los Angeles, CA) - See all my reviews

This review is from: Topological Spaces: From Distance to Neighborhood (Undergraduate Texts in Mathematics) (Hardcover)

It starts the discussion with the familiar metric spaces and the real line and then
shows how convergence can be generalized. From this point, he then shows the
connection to topology. He also provides motivation for the results, exercises,
and historical sketches at the end of every chapter. The writing is unusually
clear.