Complete (mathematics)

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The term complete in mathematics is used in the following broad senses:

  • An algebraic, topological or geometric structure that is closed under certain kinds of operations.
  • A structure such that any bigger structure containing it has it as a summand or split piece.

In group theory

Complete group: A group whose center is trivial and in which every automorphism is inner. Equivalently, it is a direct factor inside any group in which it is a normal subgroup.

Primary subject wiki entry: Groupprops:Complete group

In category theory

Complete category: A category that contains all small limits.

Primary subject wiki entry: Cattheory:Complete category

In ring theory

Complete intersection ring

In topology

Complete metric space

Completely metrizable space

In differential geometry

Complete Riemannian manifold