Definition:Minimal Condition/Subset Ordering

Definition

Let $S$ be a set.

Let $F$ be a set of subsets of $S$.

Let $F$ be ordered by the subset relation.

Then $S$ satisfies the minimal condition on $F$ if and only if $F$ satisfies the minimal condition.

Also see

• Definition:Descending Chain Condition
• Definition:Maximal Condition on Submodules