Category:Order theory

C

• [+] Closure operators (27 P)

D

• [+] Domain theory (3 P)

F

• [+] Fixed points (3 C, 52 P)

L

• [+] Lattice theory (2 C, 29 P)

O

• [+] Ordered algebraic structures (1 C, 4 P)
• [+] Ordered groups (12 P)

O cont.

• [+] Ordinal numbers (1 C, 37 P)

S

• [+] Sorting algorithms (3 C, 57 P)

W

• [+] Wellfoundedness (21 P)

• List of order theory topics
• Glossary of order theory

*

• Order theory

A

• Alexandrov topology
• Antichain
• Aronszajn line
• Ascending chain condition
• Atom (order theory)

B

• Boolean prime ideal theorem
• Bound graph
• Bounded complete poset
• Bounded set
• Bourbaki–Witt theorem

C

• Cantor's first uncountability proof
• Causal sets
• Chain complete
• Closure operator
• Cofinal (mathematics)
• Cofinality
• Compact element
• Comparability
• Comparability graph
• Complete Boolean algebra
• Complete Heyting algebra
• Complete partial order
• Completely distributive lattice
• Completeness (order theory)
• Containment order
• Countable chain condition
• Countryman line
• Covering relation
• Critical pair

D

• Dedekind cut
• Dedekind number
• Dense order
• Dickson's lemma
• Dilworth's theorem
• Directed set
• Disjunction property of Wallman
• Distributivity (order theory)
• Duality (order theory)

E

• Embedding

F

• Fence (mathematics)
• Filter (mathematics)
• Fréchet filter
• Frink ideal

G

• Galois connection
• Graded poset
• Greatest element
• Greedoid

H

• Hasse diagram
• Hausdorff maximal principle
• Higman's lemma

I

• Ideal (order theory)
• Incidence algebra
• Infimum
• Infinite descending chain
• Infinite divisibility
• Interval (mathematics)
• Interval order

J

• Join and meet

K

• Kernel operator
• Kleene fixed-point theorem
• Kleene–Brouwer order
• Knaster–Tarski theorem
• Kruskal's tree theorem

L

• Least fixed point
• Lexicographical order
• Limit-preserving function (order theory)
• Linear continuum
• Linear extension
• Locally finite poset
• Lubell–Yamamoto–Meshalkin inequality

M

• Majorization
• Maximal element
• Möbius inversion formula
• Monomial order
• Monotonic function

N

• Non-increasing sequence

O

• Order dimension
• Order isomorphism
• Order topology

O cont.

• Order-embedding
• Ordered pair
• Ordinal scale

P

• Partially ordered set
• Partially-ordered group
• Pasch's theorem
• Pointwise order
• Poset topology
• Preorder
• Preordered class
• Prewellordering
• Prime (order theory)
• Product order
• Projection (order theory)
• Pseudoideal

Q

• Quantale

R

• Ranked poset
• Residuated mapping

S

• Schnyder's theorem
• Scott continuity
• Scott domain
• Shortlex order
• Specialization (pre)order
• Stone duality
• Strict weak ordering
• Strong antichain
• Supermodular function
• Supremum
• Suslin's problem

T

• Total order
• Trichotomy (mathematics)
• Tukey's lemma

U

• Ultrafilter
• Upper and lower bounds
• Upper set
• Upper topology

W

• Weak order of permutations
• Well-order
• Well-quasi-ordering

Z

• Zorn's lemma