Definition:Closed Set under Closure Operator/Definition 1

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:

$\map \cl T = T$

Also see

• Equivalence of Definitions of Closed Set under Closure Operator