Saw a new post on XYS. It basically says the "4-color theorem" is a global property; yet Mr. Li's Theorems and Axioms all are just talking about local properties. How to go from local to global is usually very difficult or even impossible. That's the main weakness of Mr. Li's claimed proof of the "4-color" theorem.

I completely agree. I think in calculus, most of the discussion are local. There are two cases where it is easy to go from local to global: (1) when things are linear (this is the topics of linear algebra and linear functional analysis); (2) when things are convex in some sense.