Frames with transitive structures
The purpose of the paper is to give a point-free variant of the theory of (quasi-)uniformities with transitive bases. For this, the authors consider a frame (i.e. a complete lattice satisfying the distributive law \(x\wedge\vee S=\vee\{x\wedge s\mid s\in S\}\) for \(x\in L\), \(S\subset L)\). Now a (quasi-)uniformity with a base of transitive entourages is suitably defined on \(L\) and the properties of this structure are studied.
scientific article; zbMATH DE number 1747766