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.
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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
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Morón, M.A., Ruiz Del Portal, F.R. Ultrametrics and infinite dimensional whitehead theorems in shape theory. Manuscripta Math 89, 325–333 (1996). https://doi.org/10.1007/BF02567521
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DOI: https://doi.org/10.1007/BF02567521