From Gonthier (2008): "Definitions: A planar map is a set of pairwise disjoint subsets of the plane, called regions. A simple map is one whose regions are connected open sets. Two regions of a map are adjacent if their respective closures have a common point that is not a corner of the map. A point is a corner of a map if and only if it belongs to the closures of at least three regions. Theorem: The regions of any simple planar map can be colored with only four colors, in such a way that any two adjacent regions have different colors." Gonthier, Georges (2008), „Formal Proof—The Four-Color Theorem”(PDF), Notices of the American Mathematical Society, 55 (11): 1382—1393, MR2463991
From Gonthier (2008): "Definitions: A planar map is a set of pairwise disjoint subsets of the plane, called regions. A simple map is one whose regions are connected open sets. Two regions of a map are adjacent if their respective closures have a common point that is not a corner of the map. A point is a corner of a map if and only if it belongs to the closures of at least three regions. Theorem: The regions of any simple planar map can be colored with only four colors, in such a way that any two adjacent regions have different colors." Gonthier, Georges (2008), „Formal Proof—The Four-Color Theorem”(PDF), Notices of the American Mathematical Society, 55 (11): 1382—1393, MR2463991