Principles of Topology (Dover Books on Mathematics)

This book is for the senior undergraduate, beginning graduate student or the enthusiastic high schooler.I found it to be written in a very clear lucid style. The book engaged me and drew me in.It is about the same level as Munkres' text but more down to earth with no compromise on rigor.It covers metric and topological spaces; connected sets and metrizable spaces (Urysohn's lemma).I really like this text and at this level is probably the best book on topology( and I have read a fair number of books on this subject).

This book will teach you topology. It does an excellent job of rigorously covering the major topics while being very readable. I can tell you that I've downloaded pdf's of pretty much every topology textbook available and have still found this one to be the best. It's just a coincidence that it happens to be cheap and a nice paperback (it's nothing like dover's collection of terrible cheap translated textbooks). I would recommend Croom and Munkres to be the standard 2-book combination for topology from the undergraduate to graduate level.

I am a freshman undergraduate student and I have liked topology since high school. As soon as I got into college I knew I will take the topology course whenever they offer one. So my second semester, there was a topology course offered and since I did not have all the prereqs for it I talked to the teacher to get approved for the course.Though I really liked the course and every class I found something fascinating, it was a bit hard to get my formal proofs done 100% correct. So I was looking for an additional aid to my textbook, which did not have too many proofs written on it. I came across this one and decided to order it together with some other ones.The book is a nice introduction to point set topology for undergraduate level, however it did not satisfy my needs much, since the main purpose of my purchase was getting to see more formal proofs.Overall, it is very engaging and well written and I would certainly recommend it to beginner topologists.

We used this text in my undergrad topology class. The professor assigned some of the questions from each section but recommended we do or at least attempt all of them. And he was right. You get so much out of this book by doing every problem, you will thoroughly understand each and every definition after solving the problems as each problem requires you to gain further understanding of the definitions.The book is clearly written and full of examples using spaces as concrete as the real numbers all the way to seemingly bizarre abstract spaces. Due to personal reasons I was away from studying pure mathematics for nearly ten years, I decided to pick it back up again during the pandemic lock-down. Fortunately, this book is so well-written that I was able to re-teach myself basic point-set topology and get myself to the point where I could start studying more advanced texts.The structure of the book provides the perfect bridge from the world of beginner real analysis to point-set topology. Starting off with a review of properties of the real numbers and then moving on to metric spaces. The transition from real number spaces to metric spaces is done so seamlessly that anyone who has had a first course in real analysis should not have any trouble making the leap.Croom takes concepts developed in metric spaces and extends them naturally to the more abstract concept of general topological spaces. This is done so well that many of the proofs for general topological spaces can be seen as generalizations of a similar proof in the metric spaces chapter.The book then has a chapter on connected spaces and compact spaces. The final chapters are an introduction to concepts that will be further explored in more advanced topology classes such as Algebraic Topology.I would recommend this book to anyone who has an interest in pure mathematics. While I would recommend at least some knowledge of real analysis, it is not strictly necessary as the material you need can all be gathered from chapter 1 (basic set theory stuff) and chapter 2 (real number line and the plane). The book is so well written that I think a very enthusiastic and dedicated advanced high school student could enjoy it, but they would need enough discipline to work through the proofs and exercises.

Amazing book

I'm an adult, self-study student, with a background in calculus, physics. I've now gone through several books on topology, and I find that even many of the undergraduate texts tend to be a bit "dense," in that they introduce too much, too fast. Croom's textbook takes a very step-by-step, hand-holding approach to introducing topology, focusing on concrete examples, yet still having a reasonable amount of rigor. (Of nine chapters, he doesn't even formally get to topology until Chapter 4. The first three chapters are a general intro, open and closed sets, and metric spaces.) The last chapter offers a basic introduction to algebraic topology. This is an excellent book for self-study, and also good for undergraduates with a physics or engineering orientation who want to get the intuitive principles, and also some sense for the formal math. Students (including undergrads) who are really strong on abstract math might benefit from the more intensive and detailed treatments found in other texts; but even they might find Croom's book useful to fall back on when they get stuck on some basic concept. Croom includes historical discussions of the foundations of topology, which is also helpful. He also includes a glossary of mathematical symbols up front, which is very helpful for trying to keep track of all the new notations involved. There are lots of solved problems, and also problems for students to work out, although solutions for those would be helpful in some future edition.

I really like this book for a first course in topology. It has the right level and balance of subjects. The book has been very hard to find for a number of years but has now been republished by Thomson Learning in Singapore. The new ISBN is 981-243-288-4.

Way too brief for self teaching

The book contains also exercises, that are useful to better understand concepts

Grand effort de clarté de nombreux exemples à un prix doverun seul regret les exos ne sont pas corrigés à compléter par le Shaum de Seymour Lipschutz pouf exosplus accessible que le Bert Mendelsonn

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Bought it for 999/-. Amazon gave the best deal I could get on this book.According to my sister, it's a useful book for PG students.I don't know if it's useful for layman in math like me to learn topology. I tried reading but gave up quickly.Anyway, I give it 5 stars as It's useful for sis and I got at the best deal price.Book paper quality is good too. No complaints there. It was delivered in two days to Kerala.Overall good experience.PS: People who want to buy,Please preview the book content before purchasing as I'm unable to recommend academic books like these.

Seul Fred Croom est l'auteur.Le contenu est intéressant mais l'absence de certaines démonstration (par exemple la preuve du Théorème 8.19 p.260 sur la métrisabilité d'un espace topologique) est très regrettable !En outre l'absence de solutions aux exercice fait que ce livre n'est pas bien adapté à une étude en autodidacte.