💡 Words with a Similar Meaning to "Directed set"
Found via reverse dictionary — words that share a conceptual meaning.
| Word | Definition |
|---|---|
| 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. |
| preordernoun | An 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. |
| chainnoun | A 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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