Cover
From AoPSWiki
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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