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*-$\mathrm{HPol}_0$ 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.

Keywords

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

2010 Mathematics Subject Classification

55N99, 55P55, 55Q05

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Published 4 December 2014