Extreme point
（重定向自Extremal point）
![A convex set in light blue, and its extreme points in red.](/Images/godic/202501/12/Extreme_points.svg5041.png")
In mathematics, an extreme point of a convex set S in a real vector space is a point in S which does not lie in any open line segment joining two points of S. Intuitively, an extreme point is a "vertex" of S.
The Krein–Milman theorem is stated for locally convex topological vector spaces. The next theorems are stated for Banach spaces with the Radon–Nikodym property: