Ma. Moron et Frr. Delportal, ULTRAMETRICS AND INFINITE-DIMENSIONAL WHITEHEAD THEOREMS IN SHAPE-THEORY, Manuscripta mathematica, 89(3), 1996, pp. 325-333
We apply a Cantor completion process to construct a complete, non-Arch
imedean metric on the set of shape morphisms between pointed compacta.
In the case of shape groups we obtain a canonical norm producing a co
mplete, both left and right invariant ultrametric. On the other hand,
we give a new characterization of movability and we use these spaces o
f shape morphisms and uniformly continuous maps between them, to prove
an infinite-dimensional theorem from which we can show, in a short an
d elementary way, some known Whitehead type theorems in shape theory.