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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". *A complete set of invariants, together with which invariants are realizable, solves the classification problem, and is often a step in solving it. *A computable complete set of invariants (together with which invariants are realizable) solves both the classification problem and the equivalence problem. * A canonical form solves the classification problem, and is more data: it not only classifies every class, but gives a distinguished (canonical) element of each class. There exist many classification theorems in mathematics, as described below. ==Geometry== * Classification of Euclidean plane isometries * Classification theorem of surfaces * * Classification of two-dimensional closed manifolds * * Enriques–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 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「classification theorem」の詳細全文を読む スポンサード リンク
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