- Representation theorem
mathematics, a representation theorem is a theorem that states that every abstract structure with certain properties is isomorphicto a concrete structure.
Cayley's theoremstates that every group is isomorphic to a transformation group on some set.
Representation theorystudies properties of abstract groups via their representations as linear transformations of vector spaces.
Stone's representation theoremfor Boolean algebras states that every Boolean algebra is isomorphic to a field of sets.
**: A variant, Stone's representation theorem for lattices states that every
distributive latticeis isomorphic to a sublattice of the power setlattice of some set.
*in category theory,
Yoneda lemmaexplains how arbitrary functors into the category of sets can be seen as hom functors
*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
Riesz representation theoremis 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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