, Volume 89, Issue 1, pp 325-333

Ultrametrics and infinite dimensional whitehead theorems in shape theory

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Abstract

We apply a Cantor completion process to construct a complete, non-Archimedean metric on the set of shape morphisms between pointed compacta. In the case of shape groups we obtain a canonical norm producing a complete, both left and right invariant ultrametric. On the other hand, we give a new characterization of movability and we use these spaces of shape morphisms and uniformly continuous maps between them, to prove an infinite-dimensional theorem from which we can show, in a short and elementary way, some known Whitehead type theorems in shape theory.

The authors have been supported by DGICYT, PB93-0454-C02-02. Most of this work was done while the second author was visiting the Department of Mathematics of the University of Tennessee at Knoxville with a M.E.C. grant