In
mathematics, a cover of a
set X is a collection of sets C whose
union is X. In symbols, if C = {Uα : α ∈ A} is an
indexed family of subsets U, of X, then C is a cover if More generally, if Y is a subset of X, and C is a collection of subsets Uα of X, whose union contains Y, then C is said to be a cover of Y. i.e. C is a cover of Y if Covers are commonly used in the context of
topology. If the set X is a
topological space, we say that C is an open cover if each of its members are
open sets (i.e. each Uα is contained in T, where T is the topology on X).
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