Symmetric connectedness in \(T_0\)-quasi-metric spaces (Q2295722)

In this paper, the authors continue their studies about asymmetry in \(T_0\)-quasi-metric spaces. They introduce the concept of symmetric connectedness for \(T_0\)-quasi-metric spaces and present some methods to find symmetrically connected pairs of \(T_0\)-quasi-metric spaces. It is shown that the problem of determining the symmetrically connected components of points turns out to be easier when formulated for \(T_0\)-quasi-metric spaces induced by asymmetrically normed real vector spaces. Finally, they observe that there are natural relations between the theory of (anti)symmetrically connected \(T_0\)-quasi-metric spaces and the theory of connectedness in the sense of graph theory.