Topology and Its Applications

By William F. Basener

Discover a unique and modern treatment of topology employing a cross-disciplinary approach

Implemented recently to understand diverse topics, such as cell biology, superconductors, and robot motion, topology has been transformed from a theoretical field that highlights mathematical theory to a subject that plays a growing role in nearly all fields of scientific investigation. Moving from the concrete to the abstract, Topology and Its Applications displays both the beauty and utility of topology, first presenting the essentials of topology followed by its emerging role within the new frontiers in research.

Filling a gap between the teaching of topology and its modern uses in real-world phenomena, Topology and Its Applications is organized around the mathematical theory of topology, a framework of rigorous theorems, and clear, elegant proofs.

This book is the first of its kind to present applications in computer graphics, economics, dynamical systems, condensed matter physics, biology, robotics, chemistry, cosmology, material science, computational topology, and population modeling, as well as other areas of science and engineering. Many of these applications are presented in optional sections, allowing an instructor to customize the presentation.

The author presents a diversity of topological areas, including point-set topology, geometric topology, differential topology, and algebraic/combinatorial topology. Topics within these areas include:

• Open sets
• Compactness
• Homotopy
• Surface classification
• Index theory on surfaces
• Manifolds and complexes
• Topological groups
• The fundamental group and homology

Special "core intuition" segments throughout the book briefly explain the basic intuition essential to understanding several topics. A generous number of figures and examples, many of which come from applications such as liquid crystals, space probe data, and computer graphics, are all available from the publisher's Web site.

• Language: English
• Publisher: Wiley-Interscience
• Release date: Oct 18, 2011
• ISBN: 9780470067932

Reviews for Topology and Its Applications

[cpg_7 · Rating: 3 out of 5 stars]

Needs corrections?A student came by my office yesterday with a question about an exercise from this book that asked the reader to show that the product topology and the standard metric topology on R^2 are equivalent. The student thought he had a counterexample (a disc containing part of its boundary), and he was right as far Basener's faulty definition of the product topology was concerned. Basener defines a set to be open in the product topology if and only if its image under each projection is open.I scoured the Internet for mention of this error and came across the Zentralblatt review (which is omitted from Amazon's list of editorial reviews for this book). That review lists this error and others and states in summary: "The book is absolutely terrible."That's obviously a strong assertion, and, not having read the book, I'm in no position to confirm or deny it. Still, I felt it was important to post this note to warn potential purchasers/readers of problems with this text, and to encourage the author and publisher to fix things. Neither the publisher website nor the (apparently broken) author website nor a Google search yielded a list of errata.[8/19/2008 Update: The author's website has been fixed, and it has a list of errata. Furthermore, the author assures me that the error in the definition of the product topology has been fixed in printings after the first.]