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- In mathematics, and more specifically in order theory, several different types of ordered set have been studied.They include:
* Cyclic orders, orderings in which triples of elements are either clockwise or counterclockwise
* Lattices, partial orders in which each pair of elements has a greatest lower bound and a least upper bound. Many different types of lattice have been studied; see map of lattices for a list.
* Partially ordered sets (or posets), orderings in which some pairs are comparable and others might not be
* Preorders, a generalization of partial orders allowing ties (represented as equivalences and distinct from incomparabilities)
* Semiorders, partial orders determined by comparison of numerical values, in which values that are too close to each other are incomparable; a subfamily of partial orders with certain restrictions
* Total orders, orderings that specify, for every two distinct elements, which one is less than the other
* Weak orders, generalizations of total orders allowing ties (represented either as equivalences or, in strict weak orders, as transitive incomparabilities)
* Well-orders, total orders in which every non-empty subset has a least element
* Well-quasi-orderings, a class of preorders generalizing the well-orders (en)
- Впорядко́вана множина́ — множина для будь-яких двох елементів , якої встановлено одне з наступних відношень порядку: або ( не перевищує ),або ( не перевищує ), з наступними властивостями: 1.
* рефлексивність: будь-який елемент множини не перевершує самого себе; 2.
* антисиметричність: якщо не перевершує , а не перевершує , то елементи і збігаються; 3.
* транзитивність: якщо не перевершує , а не перевершує , то не перевершує . (uk)
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- Впорядко́вана множина́ — множина для будь-яких двох елементів , якої встановлено одне з наступних відношень порядку: або ( не перевищує ),або ( не перевищує ), з наступними властивостями: 1.
* рефлексивність: будь-який елемент множини не перевершує самого себе; 2.
* антисиметричність: якщо не перевершує , а не перевершує , то елементи і збігаються; 3.
* транзитивність: якщо не перевершує , а не перевершує , то не перевершує . (uk)
- In mathematics, and more specifically in order theory, several different types of ordered set have been studied.They include:
* Cyclic orders, orderings in which triples of elements are either clockwise or counterclockwise
* Lattices, partial orders in which each pair of elements has a greatest lower bound and a least upper bound. Many different types of lattice have been studied; see map of lattices for a list.
* Partially ordered sets (or posets), orderings in which some pairs are comparable and others might not be
* Preorders, a generalization of partial orders allowing ties (represented as equivalences and distinct from incomparabilities)
* Semiorders, partial orders determined by comparison of numerical values, in which values that are too close to each other are incomparable; a (en)
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- List of order structures in mathematics (en)
- Впорядкована множина (uk)
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