42. Definition. A poset (partially ordered set) (X, ≤) (usually written just X) is a set X together with a transitive, antisymmetric relation ≤ on X.
43. Definition. A linearly ordered set or chain is a poset (X, ≤), such that ∀a, b ∈ X, either a ≤ b or b ≤ a or a = b.
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Poset — Un poset (de l anglais partially ordered set, en français ensemble partiellement ordonné ) formalise la notion intuitive d ordre ou d arrangement entre les éléments d un ensemble. Un poset est un ensemble muni d une relation d ordre qui indique… … Wikipédia en Français
posèt — éta m (ȅ ẹ) zastar. obisk: priti na poset; včeraj je bil pri nas na posetu; vljudnostni poset / iti v posete / njegov poset nas je prijetno presenetil / pripravili smo se na poset gledališča / vstopil je nov poset gost, obiskovalec … Slovar slovenskega knjižnega jezika
poşet — is., Fr. pochette Torba Birleşik Sözler poşet çay … Çağatay Osmanlı Sözlük
Poset topology — In mathematics, the poset topology associated with a partially ordered set S (or poset for short) is the Alexandrov topology (open sets are upper sets) on the poset of finite chains of S, ordered by inclusion. Let V be a set of vertices. An… … Wikipedia
Poset — nm marécage; petite source dans un pré Doubs … Glossaire des noms topographiques en France
poset — abbr. Partially Ordered Set … Dictionary of English abbreviation
poset — po|set adj., posede; posede ærmer … Dansk ordbog
poşet çay — is. Sallama çay … Çağatay Osmanlı Sözlük
Graded poset — In mathematics, a graded poset, sometimes called a ranked poset (but see the article for an alternative meaning), is a partially ordered set (poset) P equipped with a rank function rho; from P to N compatible with the ordering (so rho;( x ) lt;… … Wikipedia
Ranked poset — In mathematics, a ranked partially ordered set (or poset) may be either:* a graded poset, or * a poset that has the property that for every element x , all maximal chains among those with x as greatest element have the same finite length, or * a… … Wikipedia
