Definition:Set Ordered by Subset Relation

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Let $S$ be a set.

Then $S$ ordered by the subset relation is the ordered set $\struct {S, \subseteq}$, where $\subseteq$ is the subset relation on $S$.

Ordering by Reverse Inclusion

Let $S$ be ordered by $\supseteq$, the dual of the subset relation $\subseteq$.

Then $S$ is said to be ordered by reverse inclusion.

Also known as

Some sources use the term ordered by inclusion for ordered by the subset relation.

Also see