Why should one study topology?

Topology lets us talk about the notion of closeness (i.e., neighborhoods), which in turn allows us to talk about things such as continuity, convergence, compactness, and connectedness without the notion of a distance. So, topology generalizes fundamental concepts of analysis/calculus.

What is studied in topology?

Topology is the mathematical study of the properties that are preserved through deformations, twistings, and stretchings of objects. Topology began with the study of curves, surfaces, and other objects in the plane and three-space.

Should I learn algebraic topology or general topology first?

General topology won’t make much sense to you unless you have a good background in Euclidean spaces or metric spaces, mathematical analysis, etc. Algebraic topology requires some background in algebraic structures such as groups, I think it doesn’t have such a difficult requirement as general topology.

What are the best books on connectedness and topology?

Gaal has an excellent section on connectedness. Very concise and clear. Wilansky has an excellent section on Baire spaces and induced topologies. It’s a little wordier than Gaal, but has many excellent exercises. Laures and Szymik write an excellent book on topology that incorporates category theory seamlessly.

Is Munkres’ book on topology worth reading?

But as a supplemental book, it is a lot of fun, and very useful. Munkres says in introduction of his book that he does not want to get bogged down in a lot of weird counterexamples, and indeed you don’t want to get bogged down in them. But a lot of topology is about weird counterexamples.

Do you have enough topology to know what your transition points need?

Now you should have enough topology to know what your transition points need to be like. Now your topology skills really come into play. There is no fix all solution to transition points, but these principles are good guides: First, check your loop flows.