An extreme point of a subset 
of a vector space 
is an extreme set 
of 
which consists of a single point 
in 
.
The collection of all extreme points of 
is sometimes denoted 
.
Extreme points play important roles in a number of areas of mathematics, e.g., in the Krein-Milman theorem which says that,
despite their moniker implying a certain degree of rarity, the collection 
can be quite large relative the host space 
.
