Saúl Rodríguez-Martín

A Cautionary Tale – Every Set is an Interval Set and an Equiset

Given a metric space (X,d) with distinct points x,y∈X, we consider the interval set Id(x,y)={z∈X:d(x,z)+d(z,y)=d(x,y)} and the equiset Ed(x,y)={z∈X:d(x,z)=d(y,z)}. The topology and geometry of these regions have been studied, in particular when the metric arises from a norm. In t...