Geodesic
The Whitehead type theorems in coarse shape theory
Homology, homotopy, and applications, Tome 15 (2013) no. 2, pp. 103-125.

Voir la notice de l'article provenant de la source International Press of Boston

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.
DOI : 10.4310/HHA.2013.v15.n2.a6
Classification : 55N99, 55P55, 55Q05
Keywords: inverse system, pro-category, pro*-category, expansion, shape, coarse shape, homotopy pro-group, $m$-equivalence 
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     title = {The {Whitehead} type theorems in coarse shape theory},
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     pages = {103--125},
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Nikola Koceić Bilan; Nikica Uglešić. The Whitehead type theorems in coarse shape theory. Homology, homotopy, and applications, Tome 15 (2013) no. 2, pp. 103-125. doi : 10.4310/HHA.2013.v15.n2.a6. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2013.v15.n2.a6/

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