Medians and betweenness
Marlow Sholander · Proceedings of the American Mathematical Society · 1954
In a recent paper [4]2 it is shown that lattices and trees have a common generalization.These systems will be called median semilattices.These semilattices are characterized below by means of segments ( § §2 and 4) and by means of betweenness ( § §3 and 4).In §5 distributive lattices are characterized by means of medians with no assumption made as to the existence of universal bounds (compare Problem 66 of [l]).In another paper [5], median semilattices are characterized in terms of a binary operation and it is shown that these systems can be imbedded in distributive lattices.