Subspaces in abstract Stone duality.
A De Morgan quasilattice is an algebra satisfying hyperidentities of the variety of De Morgan algebras (lattices). In this paper we give a functional representation of the free n-generated De Morgan quasilattice with two binary and one unary operations. Namely, we define the concept of super-De Morgan function and prove that the free De Morgan quasilattice with two binary and one unary operations on nfree generators is isomorphic to the De Morgan quasilattice of super-De Morgan functions of nvariables....
Björner (1984) a montré que l’ordre faible de Bruhat défini sur un groupe de Coxeter fini (Bourbaki 1969) est un treillis. Dans le cas du groupe symétrique ce résultat (treillis permutoèdre) a été prouvé par Guilbaud-Rosenstiehl (1963). Dans ce papier nous montrons que des propriétés connues des treillis permutoèdres peuvent s’étendre à tous les treillis de Coxeter finis et qu’inversement des propriétés démontrées sur tous les Coxeter finis ont des retombées intéressantes sur les permutoèdres....
We characterize clean elements of and show that is clean if and only if there exists a clopen sublocale in such that . Also, we prove that is clean if and only if has a clean prime ideal. Then, according to the results about we immediately get results about
We investigate the lattice of machine invariant classes. This is an infinite completely distributive lattice but it is not a Boolean lattice. The length and width of it is c. We show the subword complexity and the growth function create machine invariant classes.