List of order theory topics

List of order theory topics

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

Contents

Overview

Distinguished elements of partial orders

Subsets of partial orders

Special types of partial orders

Well-orders

Completeness properties

Orders with further algebraic operations

Orders in abstract algebra

Functions between partial orders

Completions and free constructions

  • Dedekind completion
  • Ideal completion

Domain theory

Orders in mathematical logic

Orders in topology


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