L'Intervalle En Theorie Des Relations; Ses Generalisations Filtre Intervallaire Et Cloture D'Une Relation

摘要: Abstract Given a chain, or total ordering ⩽, an interval can be defined in two ways : absolute and relative. An is subset I of the base, such that if x, y ∈ x ⩽ z y, then I. A relative with bound {a, b} where t. key for generalization to arbitrary relation A, notion local automorphism. bijective function f automorphism Dom Rng (range) are subsets isomorphism restriction A/Dom onto A/Rng f. Then base |A| A-interval, any A/I extensible by identity map on |A|-I; i.e. union latter still A. Any intersection A-intervals A-interval. characterization given exterval (complement interval). D A-interval F (subset base), disjoint from maximal, respect inclusion, among those sets A/D extenseible F. Every Both notions identical chain but already differ partial Two related introduced finite-val subval. The boolean union, intersection, complement finite-vals finite-vals. For circular C (x, z) = + iff (mod A) condition obtained this permutation; C-subval A-absolute exterval; intuitively subval segment, cake-portion. subval; every finite-val, not conversely. A-filter (A-ultrafilter) as usually, replacing intervals. compactable equivalent (1) I, finite A-intervals; (2) each A-ultrafilter F, associate element h (F) F; there exist finitely many corresponding covers base. Finally A-ultrafilters usual ultrafilters used extend relations: closure rationals real numbers; Stone lattice.