Ultrametric spaces, valued and semivalued groups arising from the theory of shape (Q2875959)

The present paper is based on a series of previous papers on (generalized) ultrametrics in the set of \(Sh(X,Y)\) (= the set of shape morphisms between two topological spaces \(X\) and \(Y\)). The authors investigate how these ultrametrics and the induced topologies depend on several choices (e.g., the HPol expansions used to get shape mappings). In addition the authors deal with properties of \(E(X)\), the group of shape equivalences of \(X\). So they obtain results about the completeness of \(E(X)\). In particular the authors extend previous results about compact metric spaces to general topological spaces.NEWLINENEWLINEFor the entire collection see [Zbl 1287.00022].