User:Tgaede/Books/Order Theory

Order Theory

 * Overview
 * Inequality (mathematics)
 * Maxima and minima
 * Partially ordered set
 * Preorder
 * Total order
 * Weak ordering
 * Trichotomy (mathematics)
 * Extended real number line
 * Antichain
 * Hasse diagram
 * Directed acyclic graph
 * Duality (order theory)
 * Product order


 * Distinguished Elements of Partial Orders
 * Greatest and least elements
 * Maximal and minimal elements
 * Upper and lower bounds
 * Infimum and supremum
 * Limit superior and limit inferior
 * Compact element


 * Subsets of Partial Orders
 * Cofinal (mathematics)
 * Linked set
 * Directed set
 * Centered set
 * Net (mathematics)
 * Upper set
 * Ideal (order theory)
 * Filter (mathematics)
 * Ultrafilter


 * Special Types of Partial Orders
 * Completeness (order theory)
 * Dense order
 * Distributivity (order theory)
 * Modular lattice
 * Distributive lattice
 * Completely distributive lattice
 * Ascending chain condition
 * Infinite descending chain
 * Countable chain condition
 * Knaster's condition


 * Well-Orders
 * Well-founded relation
 * Ordinal number
 * Well-quasi-ordering


 * Completeness Properties
 * Semilattice
 * Lattice (order)
 * Complete partial order
 * Bounded complete poset
 * Complete lattice
 * Knaster–Tarski theorem
 * Infinite divisibility
 * Complemented lattice
 * Dedekind–MacNeille completion


 * Functions Between Partial Orders
 * Monotonic function
 * Pointwise
 * Galois connection
 * Order embedding
 * Order isomorphism
 * Domain theory