William F. Basener

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.]… (meer)