An order-theoretic unification and generalisation of certain fundamental bijections in mathematical classification. I

The primary objective of this and the following chapter is to show that one simple results unifies and generalises a number of familiar bijections in the mathematical classification literature. These include the classical bijections concerning ultrametrics on a finite set, obtained in Benzecri (1965), Hartigan (1967), Jardine, Jardine and Sibson (1967) and Johnson (1967), as well as their several later extensions reported in Jardine and Sibson (1971), Janowitz (1978), Barthelemy, Leclerc and Monjardet (1984) and the unpublished research report Critchley and Van Cutsem (1989).