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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!

  • 0
    You might want to take a look at this related question : http://math.stackexchange.com/questions/189200/intuitive-significance-open-sets-and-software-for-learning-topology/189211#1892112012-10-04
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    This can be found in Wikipedia article on Topological space in the section [Equivalent definitions](http://en.wikipedia.org/wiki/Topological_space#Equivalent_definitions). I'll add a link to the [current revision](http://en.wikipedia.org/w/index.php?title=Topological_space&oldid=515651387#Equivalent_definitions) - in case the article will change in the future.2012-10-05

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