manuscripta mathematica

, Volume 89, Issue 1, pp 325–333 | Cite as

Ultrametrics and infinite dimensional whitehead theorems in shape theory

  • M. A. Morón
  • F. R. Ruiz Del Portal
Article

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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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • M. A. Morón
    • 1
  • F. R. Ruiz Del Portal
    • 2
  1. 1.Unidad Docente de Matemáticas, E.T.S.I. de MontesUniversidad Politécnica de MadridMadridSpain
  2. 2.Departamento de Geometría y Topología, Facultad de CC. MatemáticasUniversidad Complutense de MadridMadridSpain

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