I am not getting that what is the actual notion of topology and what are the best books of topology for beginner.
I always try to visualise the topology but I fail. I am not getting any idea.
How do I study topology?
Please explain the right way.
2026-03-27 13:24:25.1774617865
What is the need of topology?
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In my opinion topology is a relaxed geometry. Circles are too perfect, too exact, but a closed curve which is topologically identical ( homeomorphic ) to a circle will do for most applications.
For example in complex variables we learn about the Cauchy integral formula, which is an integral around a simple closed curve and the answer will not change as long as your curve is a closed and simple that is homeomorphic to a circle.
The real world is not perfectly geometric for example the earth is not a perfect sphere but you can say it is a topologically equivalent of a sphere.
When you draw a rectangle with hand, you get something which is more than likely not a rectangle but very close to one and you can prove your problems with your not so perfect rectangle.
Surprisingly, these days Topology is applied in science and statistics. So Topology is not just a pure branch of mathematics any more.