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Directed set

💡 Words with a Similar Meaning to "Directed set"

Found via reverse dictionary — words that share a conceptual meaning.

WordDefinition
ordered setnoun(mathematics) A totally ordered set.
quasiordernoun(set theory) A preorder.
upper setnoun(mathematics, order theory) A subset of a poset which contains any ascending chain which starts at any element of itself.
posetnoun(set theory, order theory) A partially ordered set.
algebraic posetnoun(algebra, order theory) A partially ordered set (poset) in which every element is the supremum of the compact elements below it.
lower setnoun(mathematics, order theory) A subset of a poset which contains any descending chain which starts at any element of itself.
total ordernoun(set theory, order theory) A partial order, ≤, (a binary relation that is reflexive, antisymmetric, and transitive) on some set S, such that any two elements of S are comparable (for any x, y ∈ S, either x ≤ y or y ≤ x).
totally ordered setnoun(set theory) A set having a specified total order.
preordernounAn order for goods or services placed in advance.
well-quasi-orderingnoun(mathematics) A preorder where every infinite sequence has an infinite increasing subsequence.
antichainnoun(set theory, order theory, graph theory) A subset, A, of a partially ordered set, (P, ≤), such that no two elements of A are comparable with respect to ≤.
partially ordered setnoun(set theory, order theory, loosely) A set that has a given, elsewhere specified partial order.
partial ordering relationnoun(set theory) A partial order.
chainnounA series of interconnected rings or links usually made of metal.
ordernoun(countable) A command.
direct systemnoun(algebra) A set of algebraic structures (which are part of a concrete category; e.g., modules) and a set of morphisms between them (e.g., module homomorphisms) which all together form a small category which is the image of a covariant functor whose domain is a directed poset.
well-ordernoun(set theory, order theory) A total order of some set such that every nonempty subset contains a least element.
supersetnoun(set theory) (symbol: ⊇) With respect to another set, a set such that each of the elements of the other set is also an element of the set.
ordered pairnoun(set theory) An object containing exactly two elements in a fixed order, so that, when the elements are different, exchanging them gives a different object. Notation: (a, b) or ⟨a,b⟩.
ordered ringnoun(algebra, order theory, ring theory) A ring, R, equipped with a total order, ≤, such that for arbitrary a, b, c ∈ R, if a ≤ b then a + c ≤ b + c, and if, additionally, 0 ≤ c, then both ca ≤ cb and ac ≤ bc.

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