When I first studied topology in 1975, one of the most popular topology books was Hocking and Young. It's still an important classic. Recently I needed some information about wild arcs, and this was the only book with the required information amongst my collection of 20 topology textbooks. (See pages 176-177.)

The first half of this book is about point-set topology, which is my main interest. The second half is about combinatorial topology, i.e. topological invariants of finite-dimensional manifolds. Most topology books are strongly focused on either point-set topology or combinatorial topology. So it's great to have a book which introduces both disciplines in as much detail as such a small book can give.

While writing a book which covers point-set topology (several hundred pages), I have found very often that Hocking and Young gives me the nicest definitions and theorems to refer to. All of the basic theorems which every mathematician should know about point-set topology are here. The proofs are nice and the diagrams are very numerous, clear and helpful. The counter-examples are well illustrated and well presented. Not many topology books have as many diagrams as this book.

Then in the second half (chapters 4 to 8), there is homotopy theory, a 25-page chapter on simplicial complexes, then simplicial homology theory and two more chapters on homology theory.

It's a topology classic from 1961, but it's still the best all-round introduction to topology at the 3rd year University level.

I purchased it for a project in alg top to do higher homotopy groups (of spheres) and the first theorem i had to prove was that pi_n(X) is abelian for n>1 but with pictures and explicit homotopies from each picture to the next. The Author did a great job at explaining the proof very self contained.

A good text, but nowhere near the level of, say, Munkres. Still, it can have an interesting exposition, at times.

I am teaching myself topology with this book right now, and I must say it has an excellent balance of motivation and rigor. The very first definition in the book reveals the implications of topology to anyone who has studied limit pts (and how connectedness is defined in terms of same). After less than a week of study, I understood the big picture better than most people I know who have taken a full course. The exercises are a little sparse, perhaps, but they generally make up for their small number with increased difficulty. I have only encountered a few exercises that I could call trivial. My only gripe is that the exercises are sometimes a little tricky to find.

Good

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.

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.

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.

数学記号が小さくなっている部分が多数あって読みにくい。

数学記号が違う文字に変換されてたり、誤植になったりしており

意味不明な内容になっている部分がある。

例えば和集合の記号はすべて大文字のUで代用されている。

結局、実際の本と確かめながら読むことになりKindleで読む意味があまり

感じられない。

I cannot recommend this book at all. It is extremely dense, and unless you are using it for study under the guidance of a qualified tutor I doubt many people could get through it - unless they know the subject already and are simply revising.

I bought this a couple of years ago to try and get a handle on topology before doing a proper OU course on the subject. I didn't get very far. Having now completed the OU course I've looked at the book again, and whereas I now understand most of the first half of the book, I still find it impenetrable.

There are better topology books out there!

Buenísimo libro de topología en ingles un clásico.