The Whitehead type theorems in coarse shape theory

Abstract

The analogues of Whitehead’s theorem in coarse shape theory, i.e., in the pointed coarse pro-category pro ∗ -HPol0 and in the pointed coarse shape category Sh ∗ , 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.