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