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Infinite intersections of open sets need not be open. For example, the intersection of all intervals of the form where is a positive integer, is the set , which is not open in the real line.

A metric space is a topological space, whose topology consists of the collection of all subsets that are unions of open balls. There are, however, topological spaces that are not metric spaces.

Properties

The union of any number of open sets, or infinitely many open sets, is open.

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