Author: Christopher Grant (Salem..
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...Read more