Representation theorem

From Wikipedia, the free encyclopedia

In mathematics, a representation theorem is a theorem that states that every abstract structure with certain properties is isomorphic to a concrete structure.

For example,

  • in algebra,
  • in category theory,
  • 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
    • the Riesz representation theorem is actually a list of several theorems; one of them identifies the dual space of C0(X) with the set of regular measures on X.