Steinitz's theorem may refer to any of the following results by German mathematician Ernst Steinitz (1871–1928): Steinitz's theorem on the graphs of three-dimensional convex polyhedra Steinitz exchange lemma on bases of finite-dimensional vector spaces Lévy–Steinitz theorem on the convergence of rearranged infinite series of vectors Several variations of Carathéodory's theorem (convex hull) on the enclosure of points in the convex hulls of other points Steinitz's theorem (field theory) on simple extensions The existence and uniqueness up to (non-unique) isomorphism of an algebraic closure of any field