Axioms of closed sets Let $S$ be a topological space. It means that collection of open subsets of $S$ satisfying the following axioms:


*

*$\varnothing$ and $S$ are open

*any union of open sets is open

*any finite intersection of open sets is open


Besides we may consider collection of closed sets of $S$. Question: can you give me an axioms of closed sets?
Thanks a lot!

Sure:


*

*$S$ and $\emptyset$ are closed

*any intersection of closed sets is closed

*any finite union of closed sets is closed

