Definition:Complete

Disambiguation

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Complete may refer to:

• 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:
  • Functionally Complete: a set of truth functions $S$ such that all possible truth functions are definable from $S$
  • Complete Proof System: a proof system for which every tautology is a theorem
  • Complete Theory: an $\LL$-theory in which, for every $\LL$-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
  • Complete Bipartite Graph: a bipartite graph $G = \struct {A \mid B, E}$ in which every vertex in $A$ is adjacent to every vertex in $B$.

• Number Theory:
  • Complete Set of Residues

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Also see

• Definition:Completion