List of order theory topics

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Order theory is a branch of mathematics that studies various kinds of objects (often binary relations) that capture the intuitive notion of ordering, providing a framework for saying when one thing is "less than" or "precedes" another.

An alphabetical list of many notions of order theory can be found in the order theory glossary. See also inequality, extreme value and mathematical optimization.

Overview[edit]

Distinguished elements of partial orders[edit]

Subsets of partial orders[edit]

Special types of partial orders[edit]

Well-orders[edit]

Completeness properties[edit]

Orders with further algebraic operations[edit]

Orders in algebra[edit]

Functions between partial orders[edit]

Completions and free constructions[edit]

Domain theory[edit]

Main article: Domain theory

Orders in mathematical logic[edit]

Orders in topology[edit]