List of order theory topics

Order theory is a branch of mathematics that studies various kinds of objects 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

Distinguished elements of partial orders

Subsets of partial orders

Cofinal and coinitial set, sometimes also called dense
Meet-dense set and join-dense set
Linked set
Directed set
centered and σ-centered set
Net (mathematics)
Upper set and lower set
Ideal and filter
*Ultrafilter

Special types of partial orders

Completeness (order theory)
Dense order
Distributivity (order theory)
*Modular lattice
*Distributive lattice
*Completely distributive lattice
Ascending chain condition
*Infinite descending chain
Countable chain condition, often abbreviated as ccc
Knaster's condition, sometimes denoted ''property ''

[Well-order]s

Completeness properties">completeness (order theory)">Completeness properties

Orders with further algebraic">abstract algebra">algebraic operations

Orders in [algebra]

Functions">Function (mathematics)">Functions between partial orders

Completions">Completion (order theory)">Completions and free constructions">free object">free constructions

Dedekind completion
Ideal completion

Domain theory

Orders in [mathematical logic]

Orders in [topology]