Order theory

Glossary of order theory

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, will suffice to denote the corresponding relational symbol, even without prior introduction. Furthermore, < will denote the strict order induced by (Wikipedia).

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Ideal (order theory) | Compact element | Graph (discrete mathematics) | Monotonic function | If and only if | Domain theory | Complete Boolean algebra | Semilattice | Associative algebra | Limit-preserving function (order theory) | Partially ordered set | Symmetric relation | Topology | Alexandrov topology | Complete partial order | Lattice (order) | Mathematical analysis | Distributivity (order theory) | Asymmetric relation | Introduction to Lattices and Order | Total order | Complete Heyting algebra | Sperner property of a partially ordered set | Transitive closure | Connected relation | Transitive reduction | Duality (order theory) | Scott domain | Directed set | Relation (mathematics) | Homogeneous relation | Completeness (order theory) | Hasse diagram | Continuous poset | Binary relation | Filter (mathematics) | Residuated mapping | Transitive relation | Preorder | Reflexive relation | Completely distributive lattice | Mathematics | Incidence algebra | Stone duality | Cartesian product | Dedekind–MacNeille completion | Closure operator | Locally finite poset | Order theory | Dense order | Galois connection | Linear extension | Complete lattice | Interval (mathematics) | Upper set | Pointless topology | Function composition | Derangement | Comparability graph | Cardinality | Antisymmetric relation | Antichain | Heyting algebra | Comparability | Quasitransitive relation | Order isomorphism | Scattered order | Boolean algebra (structure)