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Union of a finite collection of closed sets is closed
From Mathematics Is A Science
Revision as of 13:55, 31 October 2010 by imported>WikiSysop (The union of a finite collection of closed sets is closed moved to Union of a finite collection of closed sets is closed)
Prove that the union of a finite collection of closed sets is closed.
It follows from the fact that intersection of a finite collection of open sets is open. Closed sets are complement of open sets after all.
It's a part of the definition of topological space in terms of closed sets, by the way.