Definition:Strictly Minimal 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 an $\RR$-minimal element of $T$ :


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

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

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

Also see

 * Definition:Maximal Element under Relation