Cut points in metric spaces
Inspired by the corresponding concept in graph theory, the authors define two apparently different notions of cut point in a metric space \((X,d)\) then show that they are actually the same. A function \(f:X\to\mathbb R\) is a virtual cut point if \(f(x)+f(y)\geq d(x,y)\) and supp\((f)\) splits into non-empty \(A\cup B\) with \(d(a,b)=f(a)+f(b)\) when \(a\in A\) and \(b\in B\), and is a topological cut point if it is in the tight span \(T(d)\) and \(T(d)\setminus\{f\}\) is a disconnected subspace of \(\mathbb R^X\). In both the abstract and the body of the paper the tight span is misdefined.
scientific article; zbMATH DE number 5277559