\(n\)-semimetrics. (English) Zbl 0988.54029

Summary: We introduce \(n\)-semimetrics as a common extension of \(n\)-metrics and certain recent applied notions like the 3-way distance. The \(n\)-semimetrics are totally symmetric maps from \(E^{n+1}\) into \(\mathbb{R}_+\) satisfying the simplex inequality, a direct extension of the common triangle inequality. Among the examples, we study in detail certain \(n\)-semimetrics on \(\{0,1\}^m\). We give a few constructions and extend the 2-way distances.


54E25 Semimetric spaces
51K99 Distance geometry
52A99 General convexity
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