Definition:Closed Set Axioms

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Definition

Let $S$ be a set.


The closed set axioms are the conditions under which a subset $F \subseteq \mathcal P \left({S}\right)$ of the power set of $S$ consists of the closed sets of a topology on $S$:

\((C1)\)   $:$   The intersection of an arbitrary subset of $F$ is an element of $F$.             
\((C2)\)   $:$   The union of any two elements of $F$ is an element of $F$.             
\((C3)\)   $:$   $\varnothing$ is an element of $F$.             

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