Weierstrass theorem

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Several theorems are named after Karl Weierstrass. These include:

• The Weierstrass approximation theorem, also known as the Stone-Weierstrauss 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