# Category:Lower Sets

This category contains results about Lower Sets.
Definitions specific to this category can be found in Definitions/Lower Sets.

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

Let $L \subseteq S$.

Then $L$ is a lower set in $S$ if and only if:

For all $l \in L$ and $s \in S$: if $s \preceq l$ then $s \in L$.

That is, $L$ is a lower set if and only if it contains its own lower closure.

## Pages in category "Lower Sets"

The following 18 pages are in this category, out of 18 total.