# Category:Upper Closures

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

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

Let $a \in S$.

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

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

That is, $a^\succcurlyeq$ is the set of all elements of $S$ that succeed $a$.

## Subcategories

This category has only the following subcategory.

## Pages in category "Upper Closures"

The following 24 pages are in this category, out of 24 total.