Axiom:Closed Set Axioms

Definition

Let $S$ be a set.

The closed set axioms are the conditions under which a subset $F \subseteq \powerset S$ of the power set of $S$ consists of the closed sets of a topology on $S$:

\((\text C 1)\)	$:$							The intersection of an arbitrary subset of $F$ is an element of $F$.
\((\text C 2)\)	$:$							The union of any two elements of $F$ is an element of $F$.
\((\text C 3)\)	$:$							$\O$ is an element of $F$.

Also see

• Definition:Topology Defined by Closed Sets
• Axiom:Open Set Axioms