Definition:Closed Element/Definition 2

Definition

Let $\struct {S, \preceq}$ be an ordered set.

Let $\cl$ be a closure operator on $S$.

Let $x \in S$.

The element $x$ is a closed element of $S$ (with respect to $\cl$) if and only if $x$ is in the image of $\cl$:

$x \in \Img \cl$

Also see

• Equivalence of Definitions of Closed Element