Applications of transitivities of betweenness in lattice theory
Malcolm F. Smiley, William R. R. Transue · Bulletin of the American Mathematical Society · 1943
This paper is an expansion of our note Metric lattices as singular metric spaces which was presented to the Society on December 29, 1941, and which was to appear in Bull.Amer.Math.Soc.2 Numbers in square brackets refer to the list of references at the end of the paper.3 It would be interesting to characterize metric spaces among our general systems.This problem appears difficult to us, and we make no attempt to solve it.