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# Intersection of any collection of closed sets is closed

From Mathematics Is A Science

Revision as of 13:58, 31 October 2010 by imported>WikiSysop

Prove that the intersection of any collection of closed sets is closed.

It follows from the fact that the union of any collection of open sets is open. Closed sets are complements of open sets after all.

It's a part of the definition of topological space in terms of closed sets, by the way.