Definition:Quasi-Concave Total Preordering

Definition
Let $R^n$ be a real vector space.

Let $\precsim$ be a total preordering on $\R^n$.

Let $\precsim$ be such that:
 * for all $b \in \R^n$, the set $\left\{ {a \in \R^n: b \precsim a}\right\}$ is convex.

Then $\precsim$ is quasi-concave.

Also see

 * Definition:Strictly Quasi-Concave Total Preordering