Continuity of coarse shape groups

Abstract

We show that every coarse shape group can be obtained as the inverse limit of an inverse system of the groups coming from an HPol_{; ; ⋆}; ; -expansion. This provides a way of computing of these interesting topological invariants (whose algebraic structure is significantly richer than those of the homotpy and shape groups) in an easier manner. It is proven that, for inverse systems of compact polyhedra, the coarse shape group functor commutes with the inverse limit.