Editing List of order structures in mathematics

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In [[mathematics]], and more specifically in [[order theory]], several different types of [[ordered set]] have been studied.
They include:
* [[Cyclic order]]s, orderings in which triples of elements are either clockwise or counterclockwise
* [[Lattice (order)|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 set]]s (or ''posets''), orderings in which some pairs are comparable and others might not be
* [[Preorder]]s, a generalization of partial orders allowing ties (represented as equivalences and distinct from incomparabilities)
* [[Semiorder]]s, 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 order]]s, orderings that specify, for every two distinct elements, which one is less than the other
* [[Weak order]]s, generalizations of total orders allowing ties (represented either as equivalences or, in strict weak orders, as transitive incomparabilities)
* [[Well-order]]s, total orders in which every non-empty subset has a least element
* [[Well-quasi-ordering]]s, a class of preorders generalizing the well-orders

==See also==

* [[Glossary of order theory]]
* [[List of order theory topics]]

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[[Category:Order theory]]