On the 90-degree-lemma

Abstract

In their technical report “On the bitopological nature of Stone duality” Jung and Moshier axiomatise a bitopological space as a d-frame, which can equivalently be described as a partial frame, a structure with two orders, one being a special Scott domain and the other a complete lattice.
The rich interaction of these two orders arises from a ternary operation on distributive lattices and is informally known as the 90-degree-lemma. Motivation for considering a second order originates in Belnap’s four-valued logic. The infinitary connections of the two orders are based on a set of axioms which are derived from the Stone duality for bitopological spaces. In this paper it is shown that the axioms given by Jung and Moshier contain some previously unknown redundancies. The redundancies yield an isomorphism of two categories, one having special Scott domains as objects and the other a certain type of complete lattice.