Ultrametrics and infinite dimensional Whitehead theorems in shape theory
The authors use a Cantor completion process to construct a complete non-Archimedean metric on the set of shape morphisms between pointed metric compacta. In the case of shape groups this produces a complete left and right invariant ultrametric on the group. This construction is analogous to the one used by the authors for the space of shape morphisms of nonpointed compacta [Shape as a Cantor completion process, Math. Z. (to appear)]. In applying this construction to pointed compacta, the authors obtain the norm on the shape groups mentioned above. This norm is used to prove a variety of known Whitehead type theorems in shape theory as well as some new results.
scientific article; zbMATH DE number 871038