Errata : «Facteurs et plans. I : Structure de finesse»
Étude des tresses de Gutmann en algèbre à valeurs
La notion de tresse de Gutmann a été introduite ([4]) pour généraliser la notion de chaîne de Gutmann qui restait souvent assez loin du protocole observé. Les tresses de Gutmann ont été étudiées ([3], [4], [6]) en considérant que les réponses au questionnaire étaient dichotomiques. Nous supposons ici que les réponses aux questions appartiennent à un ensemble fini totalement ordonné quelconque.
Extremal subobjects of complete posets
Facteurs et plans. I : Structure de finesse
f-closure algebras
Finite atomistic lattices that can be represented as lattices of quasivarieties
We prove that a finite atomistic lattice can be represented as a lattice of quasivarieties if and only if it is isomorphic to the lattice of all subsemilattices of a finite semilattice. This settles a conjecture that appeared in the context of [11].
Finite hull systems and their implication bases. (Endliche Hüllensysteme und ihre Implikationenbasen.)
Function classes and relational constraints stable under compositions with clones
The general Galois theory for functions and relational constraints over arbitrary sets described in the authors' previous paper is refined by imposing algebraic conditions on relations.
Function spaces and fixed point properties: a Galois connection.
Functional Completeness and Automorphisms.I.
Fuzzy concepts defined via residuated maps
Galois connections as left adjoint maps
Galois lattice as a framework to specify building class hierarchies algorithms
Galois Lattice as a Framework to Specify Building Class Hierarchies Algorithms
In the context of object-oriented systems, algorithms for building class hierarchies are currently receiving much attention. We present here a characterization of several global algorithms. A global algorithm is one which starts with only the set of classes (provided with all their properties) and directly builds the hierarchy. The algorithms scrutinized were developped each in a different framework. In this survey, they are explained in a single framework, which takes advantage of a substructure...
Galois theory for groups
Galois triangle theory for direct summands of modules
Galois-type connections and closure operations on preordered sets.
General algebraic geometry and formal concept analysis.
Going down in (semi)lattices of finite Moore families and convex geometries
In this paper we first study what changes occur in the posets of irreducible elements when one goes from an arbitrary Moore family (respectively, a convex geometry) to one of its lower covers in the lattice of all Moore families (respectively, in the semilattice of all convex geometries) defined on a finite set. Then we study the set of all convex geometries which have the same poset of join-irreducible elements. We show that this set—ordered by set inclusion—is a ranked join-semilattice and we...
Gram-Schmidt's orthogonalization based on the concept of generalized orthogonality