Natural metrics and their properties. I: Submetrics and overmetrics. (Russian. English summary) Zbl 1475.54015
Summary: Criteria for integer-valued function \(\mu\colon X\times X\to\{0,1,\dots\}\) to be a metric (where \(X\) is a finite set) are given. Notions of submetric, overmetric, natural and canonical metrics are introduced. Classification of metrics admitting no more than 5 values is constructed, some of their submetrics and overmetrics are described.
For Part II, see [the authors, ibid. 3, No. 1, 71-95 (2012; Zbl 1475.54016)].
For Part II, see [the authors, ibid. 3, No. 1, 71-95 (2012; Zbl 1475.54016)].
MSC:
| 54E35 | Metric spaces, metrizability |
Citations:
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