Difference between revisions of "Cover"
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A [[set]] <math>\{S_i \mid i \in I\}</math> of sets is said to '''cover''' another set <math>S</math> if <math>S \subset \bigcup_{i \in I} S_i</math>. | A [[set]] <math>\{S_i \mid i \in I\}</math> of sets is said to '''cover''' another set <math>S</math> if <math>S \subset \bigcup_{i \in I} S_i</math>. | ||
| + | The notion of covering is extremely broad, and mathematicians are often interested in covers where particular restrictions are placed on the <math>S_i</math>. For example, if we have only [[finite]]ly many of the <math>S_i</math> (the index set <math>I</math> is finite), we have a ''finite cover.'' If <math>I</math> is [[countable]], we have a ''countable cover.'' In [[topology]], one may be interested in the case that the <math>S_i</math> are [[open]] sets, in which case we have an ''open cover.'' | ||
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Latest revision as of 18:12, 26 February 2008
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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