Definition:Minimal/Element

Definition
Let $\left({S, \preceq}\right)$ be an ordered set.

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

Also defined as
Some treatments of this subject do not restrict the relation $\preceq$ to the requirement that it be an ordering.

Also known as
Some sources refer to these as atoms.

Also see

 * Equivalence of Definitions of Minimal Element


 * Definition:Maximal Element