# Category:Lower Closures

This category contains results about Lower Closures in the context of Order Theory.
Definitions specific to this category can be found in Definitions/Lower Closures.

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

Let $a \in S$.

The lower closure of $a$ (in $S$) is defined as:

$a^\preccurlyeq := \left\{{b \in S: b \preccurlyeq a}\right\}$

That is, $a^\preccurlyeq$ is the set of all elements of $S$ that precede $a$.

## Subcategories

This category has only the following subcategory.

## Pages in category "Lower Closures"

The following 21 pages are in this category, out of 21 total.