Definition:Topology Defined by Closed Sets
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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 $F$:
- $\tau = \set {U \subseteq S : S \setminus U \in F}$