# Category:Lower Sets

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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.