In [15], following a Cantor completion process, the authors give a complete, non-Archimedean metric (or ultrametric) on the set of shape morphisms between two unpointed compacta (compact metric spaces) X, Y, written Sh (X, Y). The ultrametric spaces so constructed allow to rediscover some of the more important invariants in shape theory and to introduce many others, It is clear that the construction given in {15} can be translated to the pointed case, consequently, as a particular case, we obtain a complete ultrametric that induces a norm on the shape groups of a compactum Y.
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