Ultrametrics and infinite dimensional whitehead theorems in shape theory
- 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.