Inverse limit

English

Template:Lb A subset of the Cartesian product of all the members of an inverse system, such that a member M of the subset is a sort of “cross section” of the inverse system (as fiber bundle) induced by the morphisms of it. (If $i \leq j$ in the indexing poset then $f_{i j} : A_{j} \to A_{i}$ in the inverse system and if $a_{i} \in A_{i}$ , $a_{j} \in A_{j}$ are components of M then $f_{i j} (a_{j}) = a_{i}$ ).
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Template:Lb a limit