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Trilemma

A trilemma is a difficult choice from three options, each of which is (or appears) unacceptable or unfavourable. There are two logically equivalent ways in which to express a trilemma: it can be expre

Tucker's lemma

In mathematics, Tucker's lemma is a combinatorial analog of the Borsuk–Ulam theorem, named after Albert W. Tucker. Let T be a triangulation of the closed n-dimensional ball . Assume T is antipodally s

Tube lemma

In mathematics, particularly topology, the tube lemma is a useful tool in order to prove that the finite product of compact spaces is compact.

Cartan's lemma

No description available.

Lebesgue's number lemma

In topology, Lebesgue's number lemma, named after Henri Lebesgue, is a useful tool in the study of compact metric spaces. It states: If the metric space is compact and an open cover of is given, then

Ring lemma

In the geometry of circle packings in the Euclidean plane, the ring lemma gives a lower bound on the sizes of adjacent circles in a circle packing.

Dickson's lemma

In mathematics, Dickson's lemma states that every set of -tuples of natural numbers has finitely many minimal elements. This simple fact from combinatorics has become attributed to the American algebr

Dynkin's lemma

No description available.

Liberman's lemma

Liberman's lemma is a theorem used in studying intrinsic geometry of convex surface.It is named after Joseph Liberman.

Varadhan's lemma

In mathematics, Varadhan's lemma is a result from large deviations theory named after S. R. Srinivasa Varadhan. The result gives information on the asymptotic distribution of a statistic φ(Zε) of a fa

Book of Lemmas

The Book of Lemmas is a book attributed to Archimedes by Thābit ibn Qurra, though the authorship of the book is questionable. It consists of fifteen propositions (lemmas) on circles.

Margulis lemma

In differential geometry, the Margulis lemma (named after Grigory Margulis) is a result about discrete subgroups of isometries of a non-positively curved Riemannian manifold (e.g. the hyperbolic n-spa

Ky Fan lemma

In mathematics, Ky Fan's lemma (KFL) is a combinatorial lemma about labellings of triangulations. It is a generalization of Tucker's lemma. It was proved by Ky Fan in 1952.

Schur's lemma

In mathematics, Schur's lemma is an elementary but extremely useful statement in representation theory of groups and algebras. In the group case it says that if M and N are two finite-dimensional irre

Open and closed maps

In mathematics, more specifically in topology, an open map is a function between two topological spaces that maps open sets to open sets. That is, a function is open if for any open set in the image i

Kronecker's lemma

In mathematics, Kronecker's lemma (see, e.g., , Lemma IV.3.2)) is a result about the relationship between convergence of infinite sums and convergence of sequences. The lemma is often used in the proo

Perfect group

In mathematics, more specifically in group theory, a group is said to be perfect if it equals its own commutator subgroup, or equivalently, if the group has no non-trivial abelian quotients (equivalen

Quillen's lemma

In algebra, Quillen's lemma states that an endomorphism of a simple module over the enveloping algebra of a finite-dimensional Lie algebra over a field k is algebraic over k. In contrast to a version

F. Riesz's theorem

F. Riesz's theorem (named after Frigyes Riesz) is an important theorem in functional analysis that states that a Hausdorff topological vector space (TVS) is finite-dimensional if and only if it is loc

Pumping lemma for regular languages

In the theory of formal languages, the pumping lemma for regular languages is a lemma that describes an essential property of all regular languages. Informally, it says that all sufficiently long stri

Dwork's lemma

No description available.

Gauss's lemma

Gauss's lemma can mean any of several lemmas named after Carl Friedrich Gauss:
* Gauss's lemma (polynomials) – The greatest common divisor of the coefficients is a multiplicative function
* Gauss's

Littlewood–Offord problem

In mathematical field of combinatorial geometry, the Littlewood–Offord problem is the problem of determining the number of of a set of vectors that fall in a given convex set. More formally, if V is a

Sauer–Shelah lemma

In combinatorial mathematics and extremal set theory, the Sauer–Shelah lemma states that every family of sets with small VC dimension consists of a small number of sets. It is named after and Saharon

Knaster–Kuratowski–Mazurkiewicz lemma

The Knaster–Kuratowski–Mazurkiewicz lemma is a basic result in mathematical fixed-point theory published in 1929 by Knaster, Kuratowski and Mazurkiewicz. The KKM lemma can be proved from Sperner's lem

Covering lemma

In the foundations of mathematics, a covering lemma is used to prove that the non-existence of certain large cardinals leads to the existence of a canonical inner model, called the core model, that is

Pumping lemma for context-free languages

In computer science, in particular in formal language theory, the pumping lemma for context-free languages, also known as the Bar-Hillel lemma, is a lemma that gives a property shared by all context-f

Sperner's lemma

In mathematics, Sperner's lemma is a combinatorial result on colorings of triangulations, analogous to the Brouwer fixed point theorem, which is equivalent to it. It states that every Sperner coloring

Craig interpolation

In mathematical logic, Craig's interpolation theorem is a result about the relationship between different logical theories. Roughly stated, the theorem says that if a formula φ implies a formula ψ, an

Little's lemma

No description available.

Levi's lemma

In theoretical computer science and mathematics, especially in the area of combinatorics on words, the Levi lemma states that, for all strings u, v, x and y, if uv = xy, then there exists a string w s

Finsler's lemma

Finsler's lemma is a mathematical result named after Paul Finsler. It states equivalent ways to express the positive definiteness of a quadratic form Q constrained by a linear form L. Since it is equi

Hotelling's lemma

Hotelling's lemma is a result in microeconomics that relates the supply of a good to the maximum profit of the producer. It was first shown by Harold Hotelling, and is widely used in the theory of the

Shadowing lemma

In the theory of dynamical systems, the shadowing lemma is a lemma describing the behaviour of pseudo-orbits near a hyperbolic invariant set. Informally, the theory states that every pseudo-orbit (whi

Lax-Milgram lemma

No description available.

Hilbert's lemma

Hilbert's lemma was proposed at the end of the 19th century by mathematician David Hilbert. The lemma describes a property of the principal curvatures of surfaces. It may be used to prove Liebmann's t

Thom's first isotopy lemma

In mathematics, especially in differential topology, Thom's first isotopy lemma states: given a smooth map between smooth manifolds and a closed Whitney stratified subset, if is proper and is a submer

Dehn's lemma

In mathematics, Dehn's lemma asserts that a piecewise-linear map of a disk into a 3-manifold, with the map's singularity set in the disk's interior, implies the existence of another piecewise-linear m

Siegel's lemma

In mathematics, specifically in transcendental number theory and Diophantine approximation, Siegel's lemma refers to bounds on the solutions of linear equations obtained by the construction of auxilia

Algorithmic Lovász local lemma

In theoretical computer science, the algorithmic Lovász local lemma gives an algorithmic way of constructing objects that obey a system of constraints with limited dependence. Given a finite set of ba

List of lemmas

This following is a list of lemmas (or, "lemmata", i.e. minor theorems, or sometimes intermediate technical results factored out of proofs). See also list of axioms, list of theorems and list of conje

Urysohn's lemma

In topology, Urysohn's lemma is a lemma that states that a topological space is normal if and only if any two disjoint closed subsets can be separated by a continuous function. Urysohn's lemma is comm

Danielson-Lanczos lemma

No description available.

Hua's lemma

In mathematics, Hua's lemma, named for Hua Loo-keng, is an estimate for exponential sums. It states that if P is an integral-valued polynomial of degree k, is a positive real number, and f a real func

Gauss's lemma (Riemannian geometry)

In Riemannian geometry, Gauss's lemma asserts that any sufficiently small sphere centered at a point in a Riemannian manifold is perpendicular to every geodesic through the point. More formally, let M

Kalman–Yakubovich–Popov lemma

The Kalman–Yakubovich–Popov lemma is a result in system analysis and control theory which states: Given a number , two n-vectors B, C and an n x n Hurwitz matrix A, if the pair is completely controlla

Feld-Tai lemma

No description available.

Dynkin system

A Dynkin system, named after Eugene Dynkin is a collection of subsets of another universal set satisfying a set of axioms weaker than those of 𝜎-algebra. Dynkin systems are sometimes referred to as 𝜆-

Neyman–Pearson lemma

In statistics, the Neyman–Pearson lemma was introduced by Jerzy Neyman and Egon Pearson in a paper in 1933. The Neyman-Pearson lemma is part of the Neyman-Pearson theory of statistical testing, which

Lindenbaum's lemma

In mathematical logic, Lindenbaum's lemma, named after Adolf Lindenbaum, states that any consistent theory of predicate logic can be extended to a complete consistent theory. The lemma is a special ca

Big-little-big lemma

In the mathematics of paper folding, the big-little-big lemma is a necessary condition for a crease pattern with specified mountain folds and valley folds to be able to be folded flat. It differs from

Mackey–Arens theorem

The Mackey–Arens theorem is an important theorem in functional analysis that characterizes those locally convex vector topologies that have some given space of linear functionals as their continuous d

Lindelöf's lemma

In mathematics, Lindelöf's lemma is a simple but useful lemma in topology on the real line, named for the Finnish mathematician Ernst Leonard Lindelöf.

Lindström–Gessel–Viennot lemma

In Mathematics, the Lindström–Gessel–Viennot lemma provides a way to count the number of tuples of non-intersecting lattice paths, or, more generally, paths on a directed graph. It was proved by Gesse

Kac's lemma

In ergodic theory, Kac's lemma, demonstrated by mathematician Mark Kac in 1947, is a lemma stating that in a measure space the orbit of almost all the points contained in a set of such space, whose me

Newman's lemma

In mathematics, in the theory of rewriting systems, Newman's lemma, also commonly called the diamond lemma, states that a terminating (or strongly normalizing) abstract rewriting system (ARS), that is

Borel–Cantelli lemma

In probability theory, the Borel–Cantelli lemma is a theorem about sequences of events. In general, it is a result in measure theory. It is named after Émile Borel and Francesco Paolo Cantelli, who ga

Johnson–Lindenstrauss lemma

In mathematics, the Johnson–Lindenstrauss lemma is a result named after William B. Johnson and Joram Lindenstrauss concerning low-distortion embeddings of points from high-dimensional into low-dimensi

Thom's second isotopy lemma

In mathematics, especially in differential topology, Thom's second isotopy lemma is a family version of Thom's first isotopy lemma; i.e., it states a family of maps between Whitney stratified spaces i

Mostowski collapse lemma

In mathematical logic, the Mostowski collapse lemma, also known as the Shepherdson–Mostowski collapse, is a theorem of set theory introduced by Andrzej Mostowski and.

Hautus lemma

In control theory and in particular when studying the properties of a linear time-invariant system in state space form, the Hautus lemma (after Malo L. J. Hautus), also commonly known as the Popov-Bel

Schur's lemma (Riemannian geometry)

In Riemannian geometry, Schur's lemma is a result that says, heuristically, whenever certain curvatures are pointwise constant then they are forced to be globally constant. The proof is essentially a

Gordan's lemma

Gordan's lemma is a lemma in convex geometry and algebraic geometry. It can be stated in several ways.
* Let be a matrix of integers. Let be the set of non-negative integer solutions of . Then there

Itô's lemma

In mathematics, Itô's lemma or Itô's formula (also called the Itô-Doeblin formula, especially in French literature) is an identity used in Itô calculus to find the differential of a time-dependent fun

Higman's lemma

In mathematics, Higman's lemma states that the set of finite sequences over a finite alphabet, as partially ordered by the subsequence relation, is well-quasi-ordered. That is, if is an infinite seque

Morse theory

In mathematics, specifically in differential topology, Morse theory enables one to analyze the topology of a manifold by studying differentiable functions on that manifold. According to the basic insi

Krull's separation lemma

In abstract algebra, Krull's separation lemma is a lemma in ring theory. It was proved by Wolfgang Krull in 1928.

Lovász local lemma

In probability theory, if a large number of events are all independent of one another and each has probability less than 1, then there is a positive (possibly small) probability that none of the event

Piling-up lemma

In cryptanalysis, the piling-up lemma is a principle used in linear cryptanalysis to construct linear approximations to the action of block ciphers. It was introduced by Mitsuru Matsui (1993) as an an

Lemma (mathematics)

In mathematics, informal logic and argument mapping, a lemma (plural lemmas or lemmata) is a generally minor, proven proposition which is used as a stepping stone to a larger result. For that reason,

Ogden's lemma

In the theory of formal languages, Ogden's lemma (named after ) is a generalization of the pumping lemma for context-free languages.

Diagonal lemma

In mathematical logic, the diagonal lemma (also known as diagonalization lemma, self-reference lemma or fixed point theorem) establishes the existence of self-referential sentences in certain formal t

Pyrrho's lemma

In statistics, Pyrrho's lemma is the result that if one adds just one extra variable as a regressor from a suitable set to a linear regression model, one can get any desired outcome in terms of the co

Isolation lemma

In theoretical computer science, the term isolation lemma (or isolating lemma) refers to randomized algorithms that reduce the number of solutions to a problem to one, should a solution exist.This is

Tetralemma

The tetralemma is a figure that features prominently in the logic of India.

Counting lemma

The counting lemmas this article discusses are statements in combinatorics and graph theory. The first one extracts information from -regular pairs of subsets of vertices in a graph , in order to guar

Slepian's lemma

In probability theory, Slepian's lemma (1962), named after David Slepian, is a Gaussian comparison inequality. It states that for Gaussian random variables and in satisfying , the following inequality

Interchange lemma

In the theory of formal languages, the interchange lemma states a necessary condition for a language to be context-free, just like the pumping lemma for context-free languages. It states that for ever

Robbins lemma

In statistics, the Robbins lemma, named after Herbert Robbins, states that if X is a random variable having a Poisson distribution with parameter λ, and f is any function for which the expected value

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