Classification theorem
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 issues related 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 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 provides a distinguished element of each class.
Geometry
- Classification of Platonic solids
- Classification theorems of surfaces
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- * of algebraic surfaces
- * which characterizes homeomorphisms of a compact surface
- Thurston's eight model geometries, and the
Algebra
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- — a classification theorem for semisimple rings
- Classification of Simple Lie algebras and groups
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Linear algebra
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