Given a subset 
of a vector space 
, a nonempty subset 
is called an extreme set of 
if no point of 
is an internal point of any line interval whose endpoints
are in 
except when both endpoints are in 
. Said another way, 
is an extreme set of 
if whenever 
and
 |
for 
, it necessarily follows that
.
In the event that 
consists of a single point 
of 
, 
is called an extreme point
of 
. Extreme points play an important role
in a number of areas of math, e.g., in the Krein-Milman
theorem in functional analysis.
