Category:Upper Sets

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

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

Let $U \subseteq S$.

$U$ is an upper set in $S$ if and only if:

$\forall u \in U: \forall s \in S: u \preceq s \implies s \in U$