engleski

A Complete Metric for Hyperladders

For each pair of inverse systems X, Y in a category A, over the same admissible index set, there exists a complete (ultra)metric structure on the morphism set pro_{; ; ∗ }; ; ^{; ; ∼ }; ; -A(X, Y). This yields a pair of new equivalence relations on the object class of pro_{; ; ∗ }; ; ^{; ; ∼ }; ; -A that are strictly coarser than the isomorphism classification. In the case of a category pair (C, D), where D⊆ C is dense and full, these induce classifications of C-objects which are strictly coarser than the weak shape type. As an application to compact metrizable spaces, it is proved that Borsuk's quasi-equivalence (quasi-affinity) is strictly finer than the new "weak" equivalence ("weak" affinity)

pro-category; shape; weak shape; S-equivalence; quasi-equivalence; complete metric; compactum; polyhedron.

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