List of order topics
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This is a list of order topics, by Wikipedia page.
An alphabetical list of many notions of order theory can be found in the order theory glossary. See also inequality, extreme value, optimization (mathematics), domain theory.
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Basic concepts
Distinguished elements of partial orders
- Greatest element (top, unit), Least element (bottom, zero)
- Maximal element, minimal element
- Upper bound
- Least upper bound (supremum, join)
- Greatest lower bound (infimum, meet)
- Limit superior and limit inferior
- Irreducible element
- Prime element
- Compact element
Subsets of partial orders
- Cofinal set
- Dense set
- Meet-dense and join-dense set
- Directed set
- Net (mathematics)
- Upper set and lower set
- Ideal and filter
Special types of partial orders
Well-orders
Completeness properties
- Semilattice
- Lattice
- (Directed) complete partial order, (d)cpo
- Bounded complete
- Complete lattice
- Infinite divisibility
Orders with further algebraic operations
- Heyting algebra
- Complete Heyting algebra
- Boolean algebra
- Complete Boolean algebra
- Orthocomplemented lattice
- Quantale
Orders in abstract algebra
- Partially ordered monoid
- Ordered group
- Ordered ring
- Ordered field
- Artinian
- Noetherian
- Linearly ordered group
- Monomial order
- Weak order of permutations
- Incidence algebra
Functions between partial orders
- Monotonic
- Pointwise order of functions
- Galois connection
- Order embedding
- Order isomorphism
- Closure operator
- Functions that preserve suprema/infima
Completions and free constructions
Domain theory
- Way-below relation
- Continuous poset
- Algebraic poset
- Scott information system
- Powerdomain
- Scott topology
- Scott continuity
Orders in mathematical logic
- Lindenbaum algebra
- Zorn's lemma
- Boolean prime ideal theorem
- Ultrafilter
- Ultrafilter lemma
- Infinite tree (graph theory)
- Suslin's problem
- Absorption law
- Canonical order
Orders in topology
- Stone duality
- Specialization (pre)order
- Order topology of a total order (open interval topology)
- Alexandrov topology
- Upper topology
- Scott topology
- Lawson topology
- Finer topology