Statements
A theorem, a lemma, a proposition, a corollary, a fact or an axiom.
- Concepts 5206
- Definitions 5027
- Statements 3081
- Conjectures 75
- Problems 147
- Examples 431
- Counterexamples 71
- Objects 132
- Proofs 11
- Computations 1
- Topics 1
Ideas 2401–2550 of 3081.
| Name | Kind | Subject |
|---|---|---|
| Grothendieck inequality | Theorem | Functional analysis |
| Caristi fixed-point theorem | Theorem | Operator theory |
| Fourier basis of L2 of the circle | Theorem | Harmonic analysis on Euclidean spaces |
| Real spectrum of self-adjoint operators | Theorem | Operator theory |
| Kodaira vanishing theorem | Theorem | Algebraic geometry |
| Post's theorem | Theorem | Mathematical logic and foundations |
| Recurrence and capacity of graphs | Theorem | Potential theory |
| Krein–Smulian theorem | Theorem | Functional analysis |
| Schwarz reflection principle | Theorem | Functions of a complex variable |
| Harnack's principle | Theorem | Potential theory |
| LOBPCG | Proposition | Numerical analysis |
| Propagation of singularities | Theorem | Partial differential equations |
| Feit–Higman theorem | Theorem | Geometry |
| Lie's theorems on transformation groups | Theorem | Topological groups, Lie groups |
| Wirtinger presentation | Theorem | Manifolds and cell complexes |
| Grothendieck–Lefschetz trace formula | Theorem | Algebraic geometry |
| Lie's third theorem | Theorem | Topological groups, Lie groups |
| Margulis lemma | Theorem | Differential geometry |
| Characterizations of Galois extensions | Theorem | Field theory and polynomials |
| Higman embedding theorem | Theorem | Group theory and generalizations |
| Jentzsch's theorem on positive kernels | Theorem | Integral equations |
| Lorentz's characterization of almost convergence | Theorem | Sequences, series, summability |
| Löwner's theorem | Theorem | Operator theory |
| Tucker's lemma | Lemma | Combinatorics |
| Grauert's theorem on real analytic manifolds | Theorem | Several complex variables and analytic spaces |
| Frobenius reciprocity | Theorem | Group theory and generalizations |
| Muirhead's inequality | Theorem | Real functions |
| Bessel's integral | Proposition | Special functions |
| Poisson integral formula | Theorem | Potential theory |
| CW approximation | Theorem | Algebraic topology |
| Bishop–Phelps theorem | Theorem | Functional analysis |
| Chebyshev iteration | Theorem | Numerical analysis |
| Noether's second theorem | Theorem | Mechanics of particles and systems |
| Catmull–Clark subdivision surface | Theorem | Numerical analysis |
| Bruhat decomposition of a Lie group | Theorem | Topological groups, Lie groups |
| Kneser's theorem on solution sets | Theorem | Ordinary differential equations |
| Nörlund–Rice integral | Theorem | Difference and functional equations |
| Christodoulou–Klainerman stability of Minkowski space | Theorem | Relativity and gravitational theory |
| Inverse Z-transform | Theorem | Integral transforms, operational calculus |
| Ax–Kochen theorem | Theorem | Field theory and polynomials |
| Parametric transversality theorem | Theorem | Manifolds and cell complexes |
| M. Riesz theorem on the Hilbert transform | Theorem | Harmonic analysis on Euclidean spaces |
| Mercer's theorem | Theorem | Integral equations |
| Nielsen–Thurston classification | Theorem | Manifolds and cell complexes |
| Atiyah–Bott fixed-point theorem | Theorem | Global analysis, analysis on manifolds |
| Petersen's theorem | Theorem | Combinatorics |
| Littlewood subordination theorem | Theorem | Functions of a complex variable |
| Pentagonal number theorem | Theorem | Number theory |
| Liouville–Arnold theorem | Theorem | Dynamical systems and ergodic theory |
| Positive definiteness of the energy | Theorem | Potential theory |
| Quadratic transformations of hypergeometric functions | Theorem | Special functions |
| Equivalence of Boolean rings and Boolean algebras | Theorem | Order, lattices, ordered algebraic structures |
| von Neumann mean ergodic theorem | Theorem | Operator theory |
| Playfair's axiom | Fact | Geometry |
| Tian–Todorov theorem | Theorem | Several complex variables and analytic spaces |
| Alexander's theorem on closed braids | Theorem | Manifolds and cell complexes |
| Descartes's theorem on total angular defect | Theorem | Convex and discrete geometry |
| Grauert's solution of the Levi problem for manifolds | Theorem | Several complex variables and analytic spaces |
| Levy–Desplanques theorem | Theorem | Linear and multilinear algebra; matrix theory |
| Dahlberg's theorem on harmonic measure | Theorem | Potential theory |
| Normal basis theorem | Theorem | Field theory and polynomials |
| Dold–Kan correspondence | Theorem | Category theory; homological algebra |
| Nekhoroshev estimates | Theorem | Dynamical systems and ergodic theory |
| Boundary Harnack principle | Theorem | Potential theory |
| Positive mass theorem | Theorem | Differential geometry |
| Quintuple product identity | Theorem | Number theory |
| Schwartz impossibility theorem | Theorem | Functional analysis |
| Error bound for the trapezoidal rule | Theorem | Numerical analysis |
| Stationary-action principle | Fact | Calculus of variations and optimal control; optimization |
| Shilnikov theorem | Theorem | Dynamical systems and ergodic theory |
| Kissing number problem in three dimensions | Theorem | Convex and discrete geometry |
| Dual of Lp | Theorem | Functional analysis |
| Duhamel's principle | Theorem | Ordinary differential equations |
| de Bruijn–Erdős theorem | Theorem | Geometry |
| Fatou's theorem | Theorem | Functions of a complex variable |
| Incomparability theorem | Theorem | Commutative algebra |
| Householder's method | Theorem | Numerical analysis |
| Peetre theorem on local operators | Theorem | Global analysis, analysis on manifolds |
| Dunford–Pettis theorem | Theorem | Functional analysis |
| Krein's condition | Theorem | Integral transforms, operational calculus |
| Morrey's lower semicontinuity theorem | Theorem | Calculus of variations and optimal control; optimization |
| Littlewood–Richardson rule | Theorem | Combinatorics |
| Newton–Gregory forward formula | Theorem | Approximations and expansions |
| Riemannian Penrose inequality | Theorem | Differential geometry |
| Hahn–Mazurkiewicz theorem | Theorem | General topology |
| Property P conjecture | Theorem | Manifolds and cell complexes |
| Korovkin's theorem | Theorem | Approximations and expansions |
| Spectral mapping theorem for polynomials | Theorem | Functional analysis |
| Surgery exact sequence | Theorem | Manifolds and cell complexes |
| Denjoy theorem on rotation number | Theorem | Dynamical systems and ergodic theory |
| Lagrange multipliers on Banach spaces | Theorem | Calculus of variations and optimal control; optimization |
| Lévy–Khintchine representation | Theorem | Probability theory and stochastic processes |
| Snake lemma | Lemma | Category theory; homological algebra |
| Carathéodory's extension theorem | Theorem | Measure and integration |
| Banach–Stone theorem | Theorem | Functional analysis |
| Gödel's consistency of CH and AC | Theorem | Mathematical logic and foundations |
| Coifman–Rochberg–Weiss commutator theorem | Theorem | Harmonic analysis on Euclidean spaces |
| Rubio de Francia extrapolation theorem | Theorem | Harmonic analysis on Euclidean spaces |
| Murray–von Neumann classification of factors | Theorem | Functional analysis |
| Hahn–Banach theorem | Theorem | Functional analysis |
| Dixon's identity | Theorem | Special functions |
| Banach–Mazur theorem | Theorem | Functional analysis |
| Hopf–Rinow theorem | Theorem | Differential geometry |
| Generic smoothness | Theorem | Algebraic geometry |
| Lidskii's theorem | Theorem | Operator theory |
| Frobenius theorem on real division algebras | Theorem | Associative rings and algebras |
| Structure theorem for compactly generated LCA groups | Theorem | Topological groups, Lie groups |
| Van der Corput lemma | Lemma | Harmonic analysis on Euclidean spaces |
| Green's identities | Theorem | Potential theory |
| Allard regularity theorem | Theorem | Calculus of variations and optimal control; optimization |
| Scaling rule for the Laplace transform | Proposition | Integral transforms, operational calculus |
| Narasimhan lemma | Lemma | Several complex variables and analytic spaces |
| Rademacher's theorem | Theorem | Real functions |
| Blakers–Massey theorem | Theorem | Algebraic topology |
| Bohr–Mollerup theorem | Theorem | Special functions |
| Poles of the gamma function | Theorem | Special functions |
| Tannaka–Krein duality | Theorem | Topological groups, Lie groups |
| Levitzki's theorem | Theorem | Associative rings and algebras |
| Borsuk–Ulam theorem | Theorem | Algebraic topology |
| Rogers' bound | Theorem | Convex and discrete geometry |
| Gysin sequence | Theorem | Algebraic topology |
| First main theorem of Nevanlinna theory | Theorem | Functions of a complex variable |
| Liouville's theorem for harmonic functions | Theorem | Potential theory |
| Coarea formula | Theorem | Measure and integration |
| Ky Fan minimax inequality | Theorem | Calculus of variations and optimal control; optimization |
| Weyl integration formula | Theorem | Topological groups, Lie groups |
| Mather–Yau theorem | Theorem | Several complex variables and analytic spaces |
| Moore–Osgood theorem | Theorem | Sequences, series, summability |
| Whipple's transformation | Theorem | Special functions |
| Cartan's magic formula | Proposition | Global analysis, analysis on manifolds |
| Gentzen's consistency proof | Theorem | Mathematical logic and foundations |
| Schreier refinement theorem | Theorem | Group theory and generalizations |
| Variation of parameters for difference equations | Theorem | Difference and functional equations |
| Lehmann–Scheffé theorem | Theorem | Statistics |
| Jordan curve theorem for polygons | Theorem | Geometry |
| Lenagan's theorem | Theorem | Associative rings and algebras |
| John–Nirenberg inequality | Theorem | Harmonic analysis on Euclidean spaces |
| Pontryagin duality theorem | Theorem | Abstract harmonic analysis |
| Iterative refinement | Proposition | Numerical analysis |
| Removable sets for bounded harmonic functions | Theorem | Potential theory |
| Cheeger–Gromoll splitting theorem | Theorem | Differential geometry |
| Sanov's theorem | Theorem | Probability theory and stochastic processes |
| Nonemptiness of the spectrum | Theorem | Functional analysis |
| Addition formulas for Jacobi elliptic functions | Theorem | Special functions |
| Solvability of x^n - a | Proposition | Field theory and polynomials |
| Frankel conjecture | Theorem | Several complex variables and analytic spaces |
| Castelnuovo's rationality criterion | Theorem | Algebraic geometry |
| Convolution theorem | Theorem | Harmonic analysis on Euclidean spaces |
| Feichtinger conjecture | Theorem | Harmonic analysis on Euclidean spaces |
| Cartan's classification of bounded symmetric domains | Theorem | Several complex variables and analytic spaces |