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

Rating:
Summary: I wish all math books were like this...
Review: 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.

Rating:
Summary: probably the best undergraduate level topology book
Review: 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.

Rating:
Summary: Best book ever on topology!
Review: 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!)