## $$n$$-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.

### MSC:

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

### Keywords:

simplex inequality; triangle inequality
Full Text:

### References:

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