engleski

The Whitehead type theorems in coarse shape theory

The analogues of Whitehead's theorem in coarse shape theory, i.e., in the pointed coarse pro- category pro*-HPol(0) and in the pointed coarse shape category Sh(0)*, are proved. In other words, if a pointed coarse shape morphism of finite shape dimensional spaces induces isomorphisms (epimorphism, in the top dimension) of the corresponding coarse k-dimensional homotopy pro- groups, then it is a pointed coarse shape isomorphism.

inverse system ; pro-category ; pro*-category ; expansion ; shape ; coarse shape ; homotopy pro-group ; m-equivalence

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