In mathematics, an existence theorem is a theorem which asserts the existence of a certain object. It might be a statement which begins with the phrase...

Picard's existence theorem, the Cauchy–Lipschitz theorem, or the existence and uniqueness theorem. The theorem is named after Émile Picard, Ernst Lindelöf...

Peano existence theorem, Peano theorem or Cauchy–Peano theorem, named after Giuseppe Peano and Augustin-Louis Cauchy, is a fundamental theorem which guarantees...

In class field theory, the Takagi existence theorem states that for any number field K there is a one-to-one inclusion reversing correspondence between...

Peano's existence theorem. Peano's theorem requires that the right-hand side of the differential equation be continuous, while Carathéodory's theorem shows...

In mathematics, specifically complex analysis, Riemann's existence theorem says, in modern formulation, that the category of compact Riemann surfaces...

finitely axiomatizable, while ZFC and MK are not. A key theorem of NBG is the class existence theorem, which states that for every formula whose quantifiers...

thesis that the hard part of the proof can be presented as the Model Existence Theorem (published in 1949). Henkin's proof was simplified by Gisbert Hasenjaeger...

In mathematics, the Grothendieck existence theorem, introduced by Grothendieck (1961, section 5), gives conditions that enable one to lift infinitesimal...

non-constructive proof (also known as an existence proof or pure existence theorem), which proves the existence of a particular kind of object without providing...

Black hole uniqueness theorem Cauchy–Kowalevski theorem is the main local existence and uniqueness theorem for analytic partial differential equations associated...

extension theorem (also known as Kolmogorov existence theorem, the Kolmogorov consistency theorem or the Daniell-Kolmogorov theorem) is a theorem that guarantees...

the Cauchy–Kovalevskaya theorem (also written as the Cauchy–Kowalevski theorem) is the main local existence and uniqueness theorem for analytic partial differential...

In mathematics, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then...

\end{aligned}}} There is a dual existence theorem for colimits in terms of coequalizers and coproducts. Both of these theorems give sufficient and necessary...

an (smooth projective) algebraic curve. Under the name Riemann's existence theorem a deeper result on ramified coverings of a compact Riemann surface...

layers, making it "deeper." It is important to note that these are existence theorems. They guarantee that a network with the right structure exists, but...

this perspective, the existence of isometric embeddings given by the following theorem is considered surprising. Nash–Kuiper theorem. Let (M, g) be an m-dimensional...

theorem (convex hull), about the convex hulls of sets in R d {\displaystyle \mathbb {R} ^{d}} Carathéodory's existence theorem, about the existence of...

Banach fixed-point theorem (also known as the contraction mapping theorem or contractive mapping theorem or Banach–Caccioppoli theorem) is an important...

mathematical object matching a certain description exists is called an existence theorem. Metaphysicians of mathematics investigate whether mathematical objects...

1960) was a Japanese mathematician, best known for proving the Takagi existence theorem in class field theory. The Blancmange curve, the graph of a nowhere-differentiable...

In mathematical logic, the Löwenheim–Skolem theorem is a theorem on the existence and cardinality of models, named after Leopold Löwenheim and Thoralf...

polynomial remainder theorem and the existence part of the theorem of Euclidean division for this specific case. The polynomial remainder theorem may be used to...

theorem (proof theory) Deduction theorem (logic) Diaconescu's theorem (mathematical logic) Easton's theorem (set theory) Erdős–Dushnik–Miller theorem...

family of functions. The theorem is the basis of many proofs in mathematics, including that of the Peano existence theorem in the theory of ordinary...

given a family of vector fields, the theorem gives necessary and sufficient integrability conditions for the existence of a foliation by maximal integral...

mathematics, Hall's marriage theorem, proved by Philip Hall (1935), is a theorem with two equivalent formulations. In each case, the theorem gives a necessary and...

Löb's theorem can be proved within normal modal logic using only some basic rules about the provability operator (the K4 system) plus the existence of modal...

The mountain pass theorem is an existence theorem from the calculus of variations, originally due to Antonio Ambrosetti and Paul Rabinowitz. Given certain...