List of order topics

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.

Partial orders

• Hasse diagram
• Monotonic
• Preorder
• Total order
  • Total preorder
  • Chain
• Well-order
  • Well-founded relation
  • Ordinal number
• Least upper bound
  • Greatest lower bound
  • Limit superior and limit inferior
  • Extended real number line
• Antichain
• Cofinality
• Dense
• Dedekind completion
• Infinite descending chain
  • Ascending chain condition
• Lattice
  • Knaster-Tarski theorem
• Boolean algebra
  • Boolean ring
  • Kleene algebra
• Heyting algebra
  • Pointless topology
• Galois connection
• Relative complement
• Incidence algebra

In abstract algebra

• Ordered group
  • Archimedean property
• Ordered field
• Artinian
• Noetherian
• Linearly ordered group

In mathematical logic

• Zorn's lemma
  • Hausdorff maximality theorem
• Boolean prime ideal theorem
• Suslin's problem

Directed set

• Net (mathematics)
• Filter (mathematics)
• Directed acyclic graph

Referenced By