Semilattices with sectionally antitone bijections

Ivan Chajda, Sándor Radeleczki

We study $\vee$-semilattices with the greatest element 1 where on each interval $[a,1]$ an antitone bijection is defined. We characterize these semilattices by means of two induced binary operations proving that the resulting algebras form a variety. The congruence properties of this variety and the properties of the underlying semilattices are investigated.