A more important Galois connection between distance functions and inequality relations

Abstract

In a former paper, by using the ideas of R. DeMarr, the second author established a useful Galois connection between distance functions on \(X\) and inequality relations on \(X \times \mathbb{R}\). Now, by using the ideas of A. Brøndsted, M. Altman and the second author, we establish a more important Galois connection between distance functions and inequality relations on the same set \(X\).