ELA, Volume 3, pp. 23-30, March 1998, abstract.

Ultrametric sets in Euclidean point spaces

Miroslav Fiedler


Finite sets S of points in a Euclidean space the mutual distances of 
which satisfy the ultrametric inequality 

r(A,B) =< max {r(A,C), r(C,B)} 

for all points in S are investigated and geometrically characterized. 
Inspired by results on ultrametric matrices and previous results on 
simplices, connections with so-called centered metric trees as well 
as with strongly isosceles right simplices are found.