manuscripta mathematica

, Volume 89, Issue 1, pp 325-333

First online:

Ultrametrics and infinite dimensional whitehead theorems in shape theory

  • M. A. MorónAffiliated withUnidad Docente de Matemáticas, E.T.S.I. de Montes, Universidad Politécnica de Madrid
  • , F. R. Ruiz Del PortalAffiliated withDepartamento de Geometría y Topología, Facultad de CC. Matemáticas, Universidad Complutense de Madrid

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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.