Introduction to Topology

Rating:
Summary: excellent introduction to topology
Review: I used this book to teach myself the basics of point-set topology and homotopy theory. What makes this book so great is that the author doesn't waste words in delving into the heart of a concept, while providing insight into it. A good collection of interesting problems, most with solutions in the back of the book. This makes this book very good for self study. If you liked Rudin, you'll probably like this book as well, as it is written in a similar style. If someone knows of a better introduction, do let me know.

Rating:
Summary: A solid introduction
Review: This book is divided into two parts: an introduction to topology, using metric spaces to motivate the definition of a topological space, and the algebraic applications of topology (such as homotopy theory and Jordan's theorem). The good things about it is its strong geometrical flavor and short and to-the-point explanations, which are nevertheless very good. Another excellent thing is the large number of exercises, most of which have full solutions (!) and/or hints at the end of the book. The chapter on metric spaces is also very informative, and stresses the many uses these spaces have in mathematics. However, the book does not really go into detail, especially when dealing with topological spaces. This is fine if you're looking for an introduction to topology (as the name implies . . . ) but it makes the book unsuitable as a reference. All-in-all a very "cute" book - as cute as introduction-to-topology books get!

Rating:
Summary: exceptionally well organized
Review: This is a lean fast introduction to topology at the third or fourth year level. Pure math types only. The book is terse but the topics are selected with care and one things leads to the next. The proofs are sufficiently detailed. Nearly every exercise has a solution in the back. The clearest exposition of the fundamental group I've seen.

Rating:
Summary: Good grad school prep.
Review: This is the usual text for introductory Topology at UCLA, where I took the course. The authors (who teach at UCLA) have "if you haven't chewed through every syllable you are not learning" mentality. In short, the book is terse and demands a lot from the reader. Looking back, this was great preparation for graduate school and is probably the best philosophy for the serious undergrad. The book contains all of the information one needs for an introductory course, but absolutely no more. Not a single character is wasted on "extraneous" explanation. Be ready for battle when opening this one, but it's worth it.

Rating:
Summary: Good grad school prep.
Review: This is the usual text for introductory Topology at UCLA, where I took the course. The authors (who teach at UCLA) have "if you haven't chewed through every syllable you are not learning" mentality. In short, the book is terse and demands a lot from the reader. Looking back, this was great preparation for graduate school and is probably the best philosophy for the serious undergrad. The book contains all of the information one needs for an introductory course, but absolutely no more. Not a single character is wasted on "extraneous" explanation. Be ready for battle when opening this one, but it's worth it.