Upper semicontinuous extensions of binary relations (Q1850152)

The notion of consistency in binary relations is considered. The authors provide sufficient conditions for the existence of upper semicontinuous extensions of consistent rather than transitive relations. For asymmetric relations, consistency and upper semicontinuity suffice. For more general relations, two sufficiency theorems, each of which uses one additional axiom is proved. The first employs a comparability property, and in second, another continuity requirement is added.