The aim of this paper is to provide necessary and sufficient continuity conditions for the existence of maximal elements of irreflexive, acyclic and transitive binary relations defined on compact sets. The results answer a question raised by Campbell and Walker [Journal of Economic Theory 50 (1990) 459–464], among others, who in fact established a sufficient continuity condition for interval or...

In symmetric groups, viewed as Coxeter groups, we show that the set of elements of minimal length in a double sided cell is the set of elements of maximal length in conjugated parabolic (i.e. Young) subgroups. We also give an interpretation of this set with tableau, using the RobinsonSchensted correspondance. We show also that the set of elements of maximal length in a two sided cell is the set...

In symmetric groups, viewed as Coxeter groups, we show that the set of elements of minimal length in a double sided cell is the set of elements of maximal length in conjugated parabolic (i.e. Young) subgroups. We also give an interpretation of these sets with tableau, using the RobinsonSchensted correspondence. We show also that the set of elements of maximal length in a two sided cell is the s...

We prove that a metric space may be realized as the set of maximal elements in a continuous dcpo if and only if it is completely metrizable by showing more generally that the space of maximal elements in a domain is always complete in a sense first introduced by Choquet.