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Some characterization theorems for the discrete holometric space. (English) Zbl 0668.51011

A discrete plane consists of the lattice points \(z=(q^ mx_ 0,q^ ny_ 0)\), where \(x_ 0,y_ 0,q\) are fixed real numbers such that \(x_ 0,y_ 0\geq 0\) and \(0<q<1\). The distance d between two lattice points \(z_ 1\) and \(z_ 2\) is defined as the number of lattice points of a path joining them. A discrete plane together with a distance is called a holometric space. The author gives a characterization of a domain and shows that domains are invariant under D-isometries. He also studies D- kernels.
Reviewer: E.Ellers

MSC:

51F99 Metric geometry
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