Definition:Strictly Maximal Element

Definition
Let $\struct {S, \RR}$ be a relational structure.

Let $T \subseteq S$ be a subset of $S$.

An element $x \in T$ is a strictly maximal element under $\RR$ of $T$ :


 * $\forall y \in T: x \not \mathrel \RR y$

Also known as
This strictly maximal relation is often referred to as a maximal relation in some expositions of this subject.

The appellation strictly maximal has been coined by so as to distinguish between this and the more mainstream concept of a maximal element which does not preclude $x \mathrel \RR x$.

Also see

 * Definition:Maximal Element


 * Definition:Strictly Minimal Element
 * Definition:Minimal Element