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In mathematics, and more particularly 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 ==See also== * List of order theory topics * Glossary of order theory 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「List of order structures in mathematics」の詳細全文を読む スポンサード リンク
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