Equitable partitions of continuum
Equivalent fuzzy sets
Necessary and sufficient conditions under which two fuzzy sets (in the most general, poset valued setting) with the same domain have equal families of cut sets are given. The corresponding equivalence relation on the related fuzzy power set is investigated. Relationship of poset valued fuzzy sets and fuzzy sets for which the co-domain is Dedekind-MacNeille completion of that posets is deduced.
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.
Existence of prime ideals and ultrafilters in partially ordered sets
Extended blocker, deletion, and contraction maps on antichains.
Extension of topological homology theories to partially orderd sets.
Extremal subobjects of complete posets
Facteurs et plans. I : Structure de finesse
Faserungen von Fahnenmengen
f-closure algebras
Field-independent representations of partially ordered sets.
Filters and annihilators in implication algebras
Filters in partially ordered sets
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.)
Finite orders and their minimal strict completion lattices
Whereas the Dedekind-MacNeille completion D(P) of a poset P is the minimal lattice L such that every element of L is a join of elements of P, the minimal strict completion D(P)∗ is the minimal lattice L such that the poset of join-irreducible elements of L is isomorphic to P. (These two completions are the same if every element of P is join-irreducible). In this paper we study lattices which are minimal strict completions of finite orders. Such lattices are in one-to-one correspondence with finite...
Finite topological spaces.
We show that the study of topological T0-spaces with a finite number of points agrees essentially with the study of polyhedra, by means of the geometric realization of finite spaces. In this paper all topological spaces are assumed to be T0.
Finite topologies and partitions.
Fixed edge theorems for complete lattices