manuscripta mathematica

, Volume 89, Issue 1, pp 325–333

Ultrametrics and infinite dimensional whitehead theorems in shape theory


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

DOI: 10.1007/BF02567521

Cite this article as:
Morón, M.A. & Ruiz Del Portal, F.R. Manuscripta Math (1996) 89: 325. doi:10.1007/BF02567521


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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© Springer-Verlag 1996