- Representation theorem
In

mathematics , a**representation theorem**is a theorem that states that every abstract structure with certain properties isisomorphic to a concrete structure.For example,

*in algebra,

**Cayley's theorem states that every group is isomorphic to a transformation group on some set.

**:Representation theory studies properties of abstract groups via their representations as linear transformations of vector spaces.

**Stone's representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to a field of sets.

**: A variant, Stone's representation theorem for lattices states that everydistributive lattice is isomorphic to a sublattice of thepower set lattice of some set.

*in category theory,

** theYoneda lemma explains how arbitrary functors into the category of sets can be seen ashom functor s

*in set theory,

**Mostowski's collapsing theorem states that every well-founded extensional structure is isomorphic to a transitive set with the ∈-relation

*in functional analysis

** theRiesz representation theorem is actually a list of several theorems; one of them identifies the dual space of "C"_{0}("X") with the set of regular measures on "X".

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2010.*

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