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Union of any collection of open sets is open
From Mathematics Is A Science
Revision as of 13:58, 31 October 2010 by imported>WikiSysop (The union of any collection of open sets is open moved to Union of any collection of open sets is open)
Prove that the union of any collection of open sets is open.
Easy... Given a point in the union, for any open set in the collection that contains the point, the point has a neighborhood from the basis of topology that lies inside. Take that neighborhood. It will lie inside the union set.
It's a part of the definition of topological space, by the way.