Proper cone

真锥是满足以下定义的锥

  • K is convex
  • K is closed
  • K is solid, which means it has nonempty interior
  • K is not pointed, which means that it contains no line ()
    We will used the Proper cone to define the generalized inequality.

Generalized inequality

Define the generalized inequality with a proper cone is below

and define a strict partial order by