Several theorems are named after

Karl Weierstrass Karl Theodor Wilhelm Weierstrass (german: link=no, Weierstraß ; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the "father of modern analysis". Despite leaving university without a degree, he studied mathematics ...

. These include: *The

Weierstrass approximation theorem Karl Theodor Wilhelm Weierstrass (german: link=no, Weierstraß ; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the "father of modern analysis". Despite leaving university without a degree, he studied mathematics ...

, of which one well known generalization is the Stone–Weierstrass theorem *The

Bolzano–Weierstrass theorem In mathematics, specifically in real analysis, the Bolzano–Weierstrass theorem, named after Bernard Bolzano and Karl Weierstrass, is a fundamental result about convergence in a finite-dimensional Euclidean space \R^n. The theorem states that each ...

, which ensures compactness of closed and bounded sets in R^''n'' *The Weierstrass

extreme value theorem In calculus, the extreme value theorem states that if a real-valued function f is continuous on the closed interval ,b/math>, then f must attain a maximum and a minimum, each at least once. That is, there exist numbers c and d in ,b/math> su ...

, 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 In transcendental number theory, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers. It states the following: In other words, the extension field \mathbb(e^, \dots, e^) has transce ...

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