Definition:Closed Set under Closure Operator/Definition 2
Jump to navigation
Jump to search
Definition
Let $S$ be a set.
Let $\cl: \powerset S \to \powerset S$ be a closure operator.
Let $T \subseteq S$ be a subset.
$T$ is closed (with respect to $\cl$) if and only if $T$ is in the image of $\cl$:
- $T \in \Img \cl$