The Four Color Theorem asserts that if a region in the plane is divided into ﬁnitely many countries, then each country may be colored either
red, green, blue, or yellow in such a way that no two countries with a common border (of positive length) get the same color. Use the Compactness
Theorem to show that this remains true even if there are inﬁnitely many
I get the general idea of this problem. But I'm not sure how to quantify the four color theorem properly. Could anyone please help?