Metric hypergraphs and metric-line equivalences

In a metric space with distance function dist, we say that v is between u and w if u,v,w are pairwise distinct dist(u,w)=dist(u,v)+dist(v,w). All triples {u,v,w} such constitute hypergraph induced by this space. answer to question posed in [3], construct an infinite family of 3-uniform hypergraphs no The line determined pair points x y the set consisting x, y, all z one x,y,z remaining two. Two pairs said be equivalent they determine same line. resulting equivalence relation metric-line equivalence. We genuinely obstacles prevent abstract from being