Glossary of order theory

Look up Appendix:Glossary of order theory in Wiktionary, the free dictionary.

This is a glossary of some terms used in various branches of mathematics that are related to the fields of order, lattice, and domain theory. Note that there is a structured list of order topics available as well. Other helpful resources might be the following overview articles:

• completeness properties of partial orders
• distributivity laws of order theory
• preservation properties of functions between posets.

In the following, partial orders will usually just be denoted by their carrier sets. As long as the intended meaning is clear from the context, ${\displaystyle \,\leq \,}$ will suffice to denote the corresponding relational symbol, even without prior introduction. Furthermore, < will denote the strict order induced by ${\displaystyle \,\leq .}$