# Category:Definitions/Lower Closures

This category contains definitions related to Lower Closures.
Related results can be found in Category: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 "Definitions/Lower Closures"

The following 13 pages are in this category, out of 13 total.