Topology

Rating:
Summary: Theoretical Dictionary
Review: An excellent book, not for those persons unfamiliar with the topic of topolgy; yet, combined with simpler texts this book is a goldmine of topological theorems and their proofs.

Rating:
Summary: A good start
Review: Very clearly written, full of examples and counterexamples, making use of pictures but never sacrificing rigor, the authors of this book have given students of topology a superb introduction to the field. Many students have been educated in topology by using this book, and it is sure to remain a classic in the field. It builds a solid understanding of the basic rudiments and intuition behind point-set, geometric, and algebraic topology. There is a lot of material covered in the book, and some very specialized subjects, such as Cech and Vietoris homology and some dimension theory, but with some preserverance and concentration, the entire book can be grasped within reasonable time constraints. Probably the only minus to the book is the lack of exercises. This is a quite serious omission, for the only way to master a subject is to work problems that require careful thought for their solution.

The beginning student of topology should probably read this book with the following mindset: try to think of ways and techniques that you would devise to study the structure of a topological space. Homotopy and homology (in various forms) are the standard techniques for doing this. These strategies have varying degrees of success, but their use in topology now seems to be reaching a saturation limit, even though the explicit calculation of homotopy groups is still a very active area. New techniques and concepts, representing sort of a "large deviation" from the standard ones discussed in this book, will be needed to make further progress in the study of complicated topological spaces. Something more is needed now, that is completely different than homology and homotopy theory, that will make more transparent the properties of these spaces. These new techniques will be somewhat radical from the standpoint of current ones, but they will be more effective from a conceptual (and computational) point of view.

Rating:
Summary: A Professional Topologist loves this book.
Review: When I was a graduate student 40 years ago there were very few texts in topology. The only two that I recall being in use were Hocking and Young and the book by Kelley. Over the years my copy of Hocking and Young has become quite worn. It is a wonderful book that gives the true flavor of topology. It is also contains a large number of topics that one can refer to later on. It becomes quite apparent very earlier that no one will be able to fully appreciate the book in the time span of one course. It is a book that must be read and reread over and over again. It is a real classic. I do not believe that it is the type of book that would be of much or any general interest but to a point set topologist it is a classic and must for his bookself. I am quite surprised over its low price. I can not help but compare it with the newer book by Munkres. I recall seeing Munkres book many years ago and disliking it. But the current edition seems much closer in flavor to HY and Munkres book is quite good. Munkres style is much clearer than HY, but both books target a very specialized group of people. Neither book is for the faint of heart and will take many years to absorb. Considering that Munkres book is 9 times as expensive as HY, HY seems to be the better buy.

Rating:
Summary: A Professional Topologist loves this book.
Review: When I was a graduate student 40 years ago there were very few texts in topology. The only two that I recall being in use were Hocking and Young and the book by Kelley. Over the years my copy of Hocking and Young has become quite worn. It is a wonderful book that gives the true flavor of topology. It is also contains a large number of topics that one can refer to later on. It becomes quite apparent very earlier that no one will be able to fully appreciate the book in the time span of one course. It is a book that must be read and reread over and over again. It is a real classic. I do not believe that it is the type of book that would be of much or any general interest but to a point set topologist it is a classic and must for his bookself. I am quite surprised over its low price. I can not help but compare it with the newer book by Munkres. I recall seeing Munkres book many years ago and disliking it. But the current edition seems much closer in flavor to HY and Munkres book is quite good. Munkres style is much clearer than HY, but both books target a very specialized group of people. Neither book is for the faint of heart and will take many years to absorb. Considering that Munkres book is 9 times as expensive as HY, HY seems to be the better buy.