A first version of this theorem was proved by Friedrich Hartogs, and as such it is known also as Hartogs's lemma and Hartogs's principle: in earlier Soviet...
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Tietze extension theorem Hartogs' extension theorem - a theorem in the theory of functions of several complex variables Isomorphism extension theorem - a...
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in 1943. Hartogs' main work was in several complex variables where he is known for Hartogs's theorem, Hartogs's lemma (also known as Hartogs's principle...
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Function of several complex variables (section Hartogs's extension theorem and Hartogs's phenomenon)
preparation theorem. A generalization of this theorem using the same method as Hartogs was proved in 2007. From Hartogs's extension theorem the domain...
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(dynamical systems) Hartogs–Rosenthal theorem (complex analysis) Hartogs's theorem (complex analysis) Hartogs's extension theorem (several complex variables)...
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Analytic function (redirect from Rigidity theorem for analytic functions)
than one variable are never discrete. This can be proved by Hartogs's extension theorem. Domains of holomorphy for single-valued functions consist of...
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Hardy–Littlewood maximal inequality. 2. Hardy space Hartogs 1. Hartogs extension theorem 2. Hartogs's theorem on separate holomorphicity harmonic A function...
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In set theory, the Schröder–Bernstein theorem states that, if there exist injective functions f : A → B and g : B → A between the sets A and B, then there...
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Affine variety (section Serre's theorem on affineness)
plane with the origin removed) is not an affine variety; cf. Hartogs' extension theorem. The subvarieties of codimension one in the affine space k n {\displaystyle...
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proof Cantor's theorem Cantor–Bernstein–Schroeder theorem Cardinality Aleph number Aleph-null Aleph-one Beth number Cardinal number Hartogs number Cartesian...
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has no poles of codimension one. This is an algebraic analog of Hartogs' extension theorem. There is also a relative version of this fact; see [2]. A morphism...
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Theory#Deformations of complex manifolds Enriques–Kodaira classification GAGA Hartogs' extension theorem Hermitian symmetric space Hodge decomposition Hopf manifold Imaginary...
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Functional analysis The Hahn–Banach theorem in functional analysis, allowing the extension of linear functionals. The theorem that every Hilbert space has an...
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cardinals between κ and its successor. (Without the axiom of choice, using Hartogs' theorem, it can be shown that for any cardinal number κ, there is a minimal...
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February 17, 1964) was an Austrian mathematician, famous for the Tietze extension theorem on functions from topological spaces to the real numbers. He also...
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holomorphic function of the remaining coordinate). The much deeper Hartogs' theorem proves that the continuity assumption is unnecessary: f {\displaystyle...
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then there is a forcing extension in which 2 ℵ 0 = κ {\displaystyle 2^{\aleph _{0}}=\kappa } . However, per König's theorem, it is not consistent to...
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S2CID 120514642, Zbl 0028.15301. In this work Severi gives his proof of the Hartogs' extension theorem. Severi, Francesco (1958), Lezioni sulle funzioni analitiche di...
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Bochner–Martinelli formula (category Theorems in complex analysis)
the Wayback Machine. In this paper Martinelli gives a proof of Hartogs' extension theorem by using the Bochner-Martinelli formula. Martinelli, Enzo (1984)...
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| = | B | {\displaystyle |A|=|B|} (a fact known as Schröder–Bernstein theorem). The axiom of choice is equivalent to the statement that | A | ≤ | B |...
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(for fixed s) and s (for fixed z), and, thus, holomorphic on C × C by Hartog's theorem. Hence, the following decomposition γ ( s , z ) = z s Γ ( s ) γ ∗ (...
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one-to-one back into that set. That the set above is nonempty follows from Hartogs' theorem, which says that for any well-orderable cardinal, a larger such cardinal...
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theory E E(X) is the membership relation of the set X Easton's theorem Easton's theorem describes the possible behavior of the powerset function on regular...
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proof Cantor's paradox Cantor's theorem Cantor–Bernstein–Schroeder theorem Cardinal number Aleph number Beth number Hartogs number Cardinality Cartesian...
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squares Padé approximant Padé table — table of Padé approximants Hartogs–Rosenthal theorem — continuous functions can be approximated uniformly by rational...
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_{n=1}^{\infty }\Omega _{n}} is also a domain of holomorphy (see Behnke-Stein theorem). If Ω 1 {\displaystyle \Omega _{1}} and Ω 2 {\displaystyle \Omega _{2}}...
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A n {\displaystyle \mathbb {A} ^{n}} when n ≥ 2: this is analogous to Hartogs's lemma in complex analysis, though easier to prove. That is, the inclusion...
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The axiom schema of replacement is not necessary for the proofs of most theorems of ordinary mathematics. Indeed, Zermelo set theory (Z) already can interpret...
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the Wayback Machine. In this paper Martinelli gives a proof of Hartogs' extension theorem by using the Bochner-Martinelli formula. Martinelli, Enzo (1944–1945)...
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be a polynomial. There is a counterpart of this theorem on the boundary, the Hartogs–Rosenthal theorem, which states that any continuous function ∂Ω can...
29 KB (5,028 words) - 10:39, 25 November 2023