Closed set
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In mathematics, a set , where is some topological space, is said to be closed if , the complement of in , is an open set. The empty set and the set X itself are always closed sets. The finite union and arbitrary intersection of closed sets are again closed.
Examples

Let X be the open interval (0, 1) with the usual topology induced by the Euclidean distance. Open sets are then of the form
 .

As a more interesting example, consider the function space (with a < b). This space consists of all realvalued continuous functions on the closed interval [a, b] and is endowed with the topology induced by the norm