Definition:Complete


 * Topology:
 * Complete Metric Space: a metric space in which every Cauchy sequence is convergent.
 * Topologically Complete Space: a Topological Space induced by a complete metric space
 * Complete Topological Group


 * Differential Geometry:
 * Complete Vector Field


 * Order Theory:
 * Complete Ordered Set: an ordered set whose subsets all admit both a supremum and an infimum
 * (also known as a Complete Lattice)


 * Dedekind Complete Set an ordered set whose non-empty subsets that are bounded above all admit a supremum
 * Chain Complete Set: an ordered set in which every chain has an upper bound
 * (also known as an inductive ordered set).


 * Lattice Theory:
 * Complete Lattice: a lattice whose subsets all admit both an supremum and an infimum
 * (also known as a Complete Ordered Set)


 * Logic:
 * Complete Proof System: a proof system for which every tautology is a theorem
 * Complete Theory: an $\mathcal L$-theory in which, for every $\mathcal L$-sentence $\phi$, either $T \models \phi$ or $T \models \neg \phi$, where $T \models \phi$ denotes semantic entailment.


 * Graph Theory:
 * Complete Graph: a simple graph such that every vertex is adjacent to every other vertex


 * Number Theory:
 * Complete Set of Residues

Also see

 * Definition:Completion