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.