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# Union of any collection of open sets is open

From Mathematics Is A Science

Jump to navigationJump to searchProve 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.