Several theorems are named after Karl Weierstrass. These include: The Weierstrass approximation theorem, of which one well known generalization is the Stone–Weierstrass theorem The Bolzano–Weierstrass theorem, which ensures compactness of closed and bounded sets in Rn The Weierstrass extreme value theorem, which states that a continuous function on a closed and bounded set obtains its extreme values The Weierstrass–Casorati theorem describes the behavior of holomorphic functions near essential singularities The Weierstrass preparation theorem describes the behavior of analytic functions near a specified point The Lindemann–Weierstrass theorem concerning the transcendental numbers The Weierstrass factorization theorem asserts that entire functions can be represented by a product involving their zeroes The Sokhatsky–Weierstrass theorem which helps evaluate certain Cauchy-type integrals See also List of topics named after Karl Weierstrass