In 4-dimensional topology, a branch of mathematics, Rokhlin's theorem states that if a smooth, orientable, closed 4-manifold M has a spin structure (or...

has been studied in detail, starting with Rokhlin's theorem for 4-manifolds, and Hirzebruch signature theorem. Given a connected and oriented manifold...

(mathematical logic) Rokhlin's theorem (geometric topology) Rolle's theorem (calculus) Rosser's theorem (number theory) Rouché's theorem (complex analysis)...

Nikolai V. Ivanov, Anatoly Vershik and Oleg Viro. Rokhlin's contributions to topology include Rokhlin's theorem, a result of 1952 on the signature of 4-manifolds...

In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential...

parity. Unimodular lattice Donaldson theory Yang–Mills equations Rokhlin's theorem Donaldson, S. K. (1983-01-01). "An application of gauge theory to...

construct Rokhlin towers where each level is probabilistically independent of the partition. The Rokhlin lemma can be used to prove some theorems. For example...

that a spin 4-manifold has signature a multiple of eight. In fact, Rokhlin's theorem implies that a smooth compact spin 4-manifold has signature a multiple...

not admit a smooth structure. This essentially demonstrates that Rokhlin's theorem holds only for smooth structures, and not topological manifolds in...

discovered by Michael Freedman in 1982. Rokhlin's theorem shows that it has no smooth structure (as does Donaldson's theorem), and in fact, combined with the...

of spheres is cyclic of order 24, first proved by Vladimir Rokhlin, implies Rokhlin's theorem that the signature of a compact smooth spin 4-manifold is...

topology, there are two Whitney embedding theorems, named after Hassler Whitney: The strong Whitney embedding theorem states that any smooth real m-dimensional...

based on the isomorphism theorem for standard Borel spaces (Kechris 1995, Theorem (15.6)). An alternate approach of Rokhlin, based on measure theory,...

Japanese and American mathematician, best known for his eponymous fixed-point theorem. Kakutani attended Tohoku University in Sendai, where his advisor was Tatsujirō...

been used in many applications using Calderón–Zygmund operators. Some theorems about Coiflets: For a wavelet system { ϕ , ϕ ~ , ψ , ψ ~ , h , h ~ , g...

in particular. Measure-preserving systems obey the Poincaré recurrence theorem, and are a special case of conservative systems. They provide the formal...

Kharlamov, V. M. (2000), "Topological properties of real algebraic varieties: Rokhlin's way.", Russian Mathematical Surveys, 55 (4): 735–814, arXiv:math/0004134...

topological restrictions (such as the Cheeger–Gromoll soul theorem or Cartan–Hadamard theorem) on geodesically complete Riemannian manifolds of positive...

differentiation theorem Lebesgue integration Lebesgue measure Infinite-dimensional Lebesgue measure Lebesgue point Lebesgue space Lebesgue–Rokhlin probability...

Russian mathematician. He is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable systems, and contributed to several...

the Rokhlin invariant, a fundamental tool in the theory of 3- and 4-dimensional manifolds. In 1961, Jan-Erik Roos published an incorrect theorem about...

maximal components of the curve.) The theorem was proved by the combined works of Vladimir Arnold and Vladimir Rokhlin. Hilbert's sixteenth problem Tropical...

large-frequency eigenfunctions of the Laplacian on a negatively-curved manifold Rokhlin's multiple mixing problem – are all strongly mixing systems also strongly...

criterion for planar dynamical systems Kuratowski's theorem, also called the Pontryagin–Kuratowski theorem, on planar graphs Pontryagin class Pontryagin duality...

Lebesgue–Rokhlin probability space Lebesgue–Stieltjes integration Lebesgue–Vitali theorem Blaschke–Lebesgue theorem Borel–Lebesgue theorem Fatou–Lebesgue...

by the Rokhlin formula for entropy. Then using the Shannon–McMillan–Breiman theorem, with its equipartition property, we obtain Lochs' theorem. A covering...

Mappings, from Leningrad University in 1972, under the direction of Vladimir Rokhlin. Due to the growing anti-Semitism in the Soviet Union, from 1972 to 1979...

simply connected, only that its fundamental group is perfect (see Hurewicz theorem). A rational homology sphere is defined similarly but using homology with...

set, but it is always a semialgebraic set: this is the Tarski–Seidenberg theorem. Related fields are o-minimal theory and real analytic geometry. Examples:...

{\displaystyle b_{ij}=(x_{j}-y_{i})A_{j}(y_{i})B_{i}(x_{j})\,}     (Schechter 1959, Theorem 1) where Ai(x) and Bi(x) are the Lagrange polynomials for ( x i ) {\displaystyle...