Convex space
In mathematics, a convex space (or barycentric algebra) is a space in which it is possible to take convex combinations of any sets of points.

Formal Definition 

A convex space can be defined as a set  equipped with a binary convex combination operation  for each  satisfying:
 
 
 
 
  (for )

From this, it is possible to define an n-ary convex combination operation, parametrised by an n-tuple , where .

Examples 

Any real affine space is a convex space. More generally, any convex subset of a real affine space is a convex space.

History 

Convex spaces have been independently invented many times and given different names, dating back at least to Stone (1949). They were also studied by Neumann (1970) and Świrszcz (1974), among others.

References 

Convex geometry
Algebraic structures