Approximation relations on the posets of pseudometrics and of pseudoultrametrics

S. I. Nykorovych


We show that non-trivial "way below" and "way above" relations on the posets of all pseudometrics and of all pseudoultrametrics on a fixed set $X$ are possible if and only if the set $X$ is finite.


pseudometric, pseudoultrametric, way below, way above

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