Cofinal Set of Subsets
A particular but important case is given if A is a subset of the power set P(E) of some set E, ordered by reverse inclusion (⊃). Given this ordering of A, a subset B of A is cofinal in A if for every a ∈ A there is a b ∈ B such that a ⊃ b.
For example, if E is a group, A could be the set of normal subgroups of finite index. Then, cofinal subsets of A (or sequences, or nets) are used to define Cauchy sequences and the completion of the group.
Read more about this topic: Cofinal (mathematics)
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