It is known that a metric space is called non-Archimedean (ultra-metric) if $d(x,y)\le\max(d(x,z),d(z,y)).$ Just out of curiosity, does there exist any metric concept such that $\min(d(x,z),d(z,y))\le d(x,y)~\forall x, y, z?.$ Will imposing such condition on metric spaces lead to any contradiction?
2026-03-22 04:44:58.1774154698
Metric concept analogous to ultra metric for minimum
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