What Is the Easiest Topology Textbook?

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In summary, the conversation discusses the difficulty of learning topology and asks for recommendations for an easy topology textbook. The concept of point set topology is briefly explained, and some classic texts are mentioned. The importance of understanding definitions and using examples to guide intuition is also emphasized. The Munkres textbook is suggested as the easiest option.
  • #1
Unassuming
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"Easiest" topology textbook/book

I am having a terrible time learning topology. Abstract algebra comes easily, as does analysis but Topology is not making any sense whatsoever to me and I honostly try harder in it than my other classes and it gets me 1/10th the progress if not thousands less.

What is the deal with Topology? I even feel like a am pretty proficient in set theory which is usually the first chapter in a Topology textbook.

Would somebody please suggest the easiest Topology text out there. I am out of solutions. I have multiple texts, I visit my professor constantly, I attend lecture, I try problems and I look for help on this forum.

Somebody fill me in. I know I am whining here but I want to hear some thoughts from people. Good or bad.
 
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  • #2


Point set topology is about generalizing the concept of a "neighborhood" and all the notions that rely of the concept of the neighborhood (continuity, convergence, etc).

Some classic texts are Munkres, Dugunji, Kelley.

I don't dislike the Dover book by Hocking & Young at all either.
 
  • #3


Thank you Quasar
 
  • #4


Judging by your posts in the HW section, I think your difficulty is stemming from a lack of understanding of the definitions. In my experience, the best way to wrap your head around all the definitions you meet in point-set topology (and there are plenty!) is by coming up with and examining examples. Fortunately, examples are very easy to come by in the beginning stages of topology. And usually thinking of all topological spaces as the metric space R^2 (with the usual Euclidean metric) is a good way to guide your intuition -- just make sure you don't take this too far, otherwise it will quickly go from an asset to a hindrance!

Edit: By the way, out of the books quasar mentioned, I would say Munkres is the easiest.
 

FAQ: What Is the Easiest Topology Textbook?

What is topology?

Topology is a branch of mathematics that studies the properties of geometric shapes and spaces that are preserved under continuous transformations.

What makes a topology textbook "easy"?

An "easy" topology textbook typically has clear and concise explanations, a logical and organized structure, and a manageable level of difficulty for beginners.

Can you recommend an easy topology textbook for beginners?

One highly recommended easy topology textbook for beginners is "Introduction to Topology: Pure and Applied" by Colin Adams and Robert Franzosa. It provides a gentle and intuitive introduction to the subject with numerous examples and exercises.

Do I need to have a strong background in mathematics to understand topology?

While a strong foundation in mathematics can certainly be helpful, it is not necessary to have a strong background in mathematics to understand topology. A good grasp of basic concepts such as sets, functions, and proofs is usually sufficient.

What are some common applications of topology?

Topology has various applications in different fields such as physics, engineering, computer science, and biology. Some common applications include analyzing data sets, studying the behavior of complex systems, and designing efficient networks.

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