nLab difunctional relation

Idea

A difunctional relation is a relation that is the union of a collection of “completely disjoint rectangles”.

Originally defined by Jacques Riguet? in 1948, nowadays they occur in computing and program specification. Their definition is reminiscent of the equations defining an inverse semigroup.

Definition

….

Properties

….

Related entries

• relation

• entire relation

• Rel

• inverse semigroup

References

• R. Backhouse, Difunctional and Block-ordered Relations, ms. 2022. (researchgate)

• R. Backhouse, J. N. Oliveira , On Difunctions, JLAMP 134 (2023). (DOI: 10.1016/j.jlamp.2023.100878; researchgate)

• Jacques Riguet?, Relations binaires, fermetures et correspondance de Galois, Bulletin de la S. M. F. tome 76 (1948) pp. 114-155. (numdam)

• Jacques Riguet?, Quelques propriétés des relations difonctionelles, CRAS (1950) pp.1999-2000.

• G. Schmidt, T. Ströhlein, Relationen und Graphen, Springer Heidelberg 1989. (section 4.4)