Classification theorem: Difference between revisions

Revision as of 23:58, 18 May 2010

Revision as of 19:13, 13 March 2014

Line 2:

In [[mathematics]], a '''classification theorem''' answers the classification problem "What are the objects of a given type, up to some equivalence?". It gives a non-redundant enumeration: each object is equivalent to exactly one class.

A few related issues to classification are the following.

*The equivalence problem is "given two objects, determine if they are equivalent".

Line 15:

* '''Classification theorem of surfaces'''

** [[Classification of two-dimensional closed manifolds]]

** [[Enriques-KodairaEnriques–Kodaira classification]] of [[algebraic surfaces]] (complex dimension two, real dimension four)

** [[Nielsen–Thurston classification]] which characterizes homeomorphisms of a compact surface

* Thurston's eight model geometries, and the [[geometrization conjecture]]

Line 21:

==Algebra==

* [[Classification of finite simple groups]]

* [[Artin–Wedderburn theorem]] — a classification theorem for semisimple rings

==Linear algebra==

* [[Finite-dimensional vector space]]s (by dimension)

* [[rank-nullityrank–nullity theorem]] (by rank and nullity)

* [[Structure theorem for finitely generated modules over a principal ideal ___domain]]

* [[Jordan normal form]]