Cover (topology)
Subsets whose union equals the whole set / From Wikipedia, the free encyclopedia
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In mathematics, and more particularly in set theory, a cover (or covering) of a set is a family of subsets of whose union is all of . More formally, if is an indexed family of subsets (indexed by the set ), then is a cover of if . Thus the collection is a cover of if each element of belongs to at least one of the subsets .
A subcover of a cover of a set is a subset of the cover that also covers the set. A cover is called an open cover if each of its elements is an open set.