Definition:Topology Defined by Closed Sets

Definition

Let $S$ be a set.

Let $F \subseteq \powerset S$ be a subset of its power set satisfying the closed set axioms.

The topology defined by $F$ is the topology whose open sets are the complements of elements of $F$:

$\tau = \set {U \subseteq S : S \setminus U \in F}$

Also see

• Topology Defined by Closed Sets is Topology