How are Kelley, Dugundji, and Willard compared to Munkres?

In summary, Kelley, Dugundji, and Willard are highly respected topology textbooks known for their concise and insightful approach. They offer different perspectives and levels of difficulty compared to Munkres, and it ultimately depends on the reader's preferences and level of understanding. It may be helpful to read a few chapters from each book to determine the best fit.
  • #1
bacte2013
398
47
Dear all,

I recently found the topology textbooks written by Kelley, Dugundji, and Willard, which I heard that they are more concise and motivational than Munkres, which is a required text for my current topology course. I actually do not like Munkres as he is very verbose, and his problems are not insightful and challenging either. Unfortunately, there is no way for me to read Kelley, Dugundji, or Willard as all of them are already checked out...I would like to hear your opinions about their pros and cons, and how they are compared to Munkres. Please help me!

P.S.
I read Armstrong, Kahn, and Hocking, and I found the last two books to be better than Munkres (I did not like Armstrong's exposition). I never read Kelley, Dugundji, and Willard...
 
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  • #2
Kelley, Dugundji, and Willard are all highly respected topology textbooks. They have a reputation for being more concise and providing more insight and challenge than Munkres. Kelley is often praised for his clear exposition of concepts and proofs. Dugundji and Willard are generally seen as rigorous and modern texts. All three books cover the same topics as Munkres but from different viewpoints and with different emphases.In terms of difficulty level, Munkres is usually considered to be easier than Kelley, Dugundji, or Willard. However, this does not necessarily mean that one is better than the other. It simply means that they cater to different audiences. For example, if you are a beginner in topology, Munkres may be more suitable for you than Kelley, Dugundji, or Willard. On the other hand, if you already have some background in topology and need to brush up on your skills, then the latter three books may be more suitable.In conclusion, it really depends on your level of understanding and what you want to get out of the book. If it is available, it is probably worth reading at least a few chapters of each book to decide which one you prefer.
 

1. How do the textbooks by Kelley, Dugundji, and Willard compare to Munkres?

These textbooks are all commonly used in undergraduate topology courses, but they differ in their level of difficulty and approach. Munkres is considered to be the most beginner-friendly and has a more intuitive presentation of the concepts. Kelley and Dugundji are more rigorous and better suited for students with a strong mathematical background. Willard is the most advanced and is commonly used for graduate level courses.

2. Which textbook is the most comprehensive?

Willard is generally considered to be the most comprehensive textbook, covering a wide range of topics in topology including point-set topology, algebraic topology, and differential topology. Munkres is also quite comprehensive, but it focuses more on point-set topology.

3. Which textbook is the easiest to understand?

Munkres is often considered to be the easiest to understand, as it uses clear and concise language and provides many examples and exercises. It also has a more visual approach, which can be helpful for students who are new to topology.

4. Which textbook is the most popular among students and teachers?

Munkres is the most commonly used textbook in undergraduate topology courses, both among students and teachers. It is known for its clarity and accessibility, making it a popular choice for introductory courses.

5. Are there any major differences between the textbooks?

While all of these textbooks cover the same fundamental concepts in topology, they differ in their level of rigor and depth of coverage. Munkres is more accessible for beginners, while Kelley, Dugundji, and Willard are better suited for more advanced students. Additionally, each textbook has its own unique style and approach to presenting the material, so it is important to choose the one that best fits your learning style.

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