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Cover

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A set \{S_i \mid i \in I\} of sets is said to cover another set S if S \subset \bigcup_{i \in I} S_i.

The notion of covering is extremely broad, and mathematicians are often interested in covers where particular restrictions are placed on the S_i. For example, if we have only finitely many of the S_i (the index set I is finite), we have a finite cover. If I is countable, we have a countable cover. In topology, one may be interested in the case that the S_i are open sets, in which case we have an open cover.

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