5.4 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| List of lemmas | 1/1 | https://en.wikipedia.org/wiki/List_of_lemmas | reference | science, encyclopedia | 2026-05-05T08:15:23.303385+00:00 | kb-cron |
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 conjectures.
== Algebra ==
Abhyankar's lemma Aubin–Lions lemma Bergman's diamond lemma Fitting lemma Injective test lemma Hua's lemma (exponential sums) Krull's separation lemma Schanuel's lemma (projective modules) Schwartz–Zippel lemma Shapiro's lemma Stewart–Walker lemma (tensors) Whitehead's lemma (Lie algebras) Zariski's lemma
=== Algebraic geometry === Abhyankar's lemma Fundamental lemma (Langlands program)
=== Category theory ===
Five lemma Horseshoe lemma Nine lemma Short five lemma Snake lemma Splitting lemma Yoneda lemma
=== Linear algebra === Matrix determinant lemma Matrix inversion lemma
=== Group theory === Burnside's lemma also known as the Cauchy–Frobenius lemma Frattini's lemma (finite groups) Goursat's lemma Mautner's lemma (representation theory) Ping-pong lemma (geometric group theory) Schreier's subgroup lemma Schur's lemma (representation theory) Zassenhaus lemma
=== Polynomials === Gauss's lemma (polynomials) Schwartz–Zippel lemma
=== Ring theory and commutative algebra === Artin–Rees lemma Hensel's lemma (commutative rings) Nakayama lemma Noether's normalization lemma Prime avoidance lemma
=== Universal algebra === Jónsson's lemma
== Analysis ==
Fekete's lemma Fundamental lemma of the calculus of variations Hopf lemma Sard's lemma (singularity theory) Stechkin's lemma (functional and numerical analysis) Vitali covering lemma (real analysis) Watson's lemma
=== Complex analysis === Estimation lemma (contour integrals) Hartogs's lemma (several complex variables) Jordan's lemma Lemma on the Logarithmic derivative Schwarz lemma
=== Fourier analysis === Riemann–Lebesgue lemma
=== Differential equations === Borel's lemma (partial differential equations) Grönwall's lemma Lax–Milgram lemma Pugh's closing lemma Weyl's lemma (Laplace equation) (partial differential equations)
=== Differential forms === Poincaré lemma of closed and exact differential forms
=== Functional analysis === Cotlar–Stein lemma Ehrling's lemma Riesz's lemma
=== Mathematical series === Abel's lemma Kronecker's lemma
=== Numerical analysis === Bramble–Hilbert lemma Céa's lemma
== Applied mathematics ==
Danielson–Lanczos lemma (Fourier transforms) Farkas's lemma (linear programming) Feld–Tai lemma (electromagnetism) Little's lemma (queuing theory) Finsler's lemma
=== Control theory === Finsler's lemma Hautus lemma Kalman–Yakubovich–Popov lemma
=== Computational complexity theory === Isolation lemma Switching lemma
==== Cryptography ==== Forking lemma Leftover hash lemma Piling-up lemma (linear cryptanalysis) Yao's XOR lemma
==== Formal languages ==== Interchange lemma Newman's lemma (term rewriting) Ogden's lemma Pumping lemma sometimes called the Bar-Hillel lemma
=== Microeconomics === Hotelling's lemma Shephard's lemma
== Combinatorics == Cousin's lemma (integrals) Dickson's lemma Littlewood–Offord lemma Pólya–Burnside lemma Sperner's lemma Ky Fan lemma (combinatorial geometry)
=== Graph theory ===
Berge's lemma Counting lemma Crossing lemma Expander mixing lemma Handshaking lemma Kelly's lemma Kőnig's lemma Szemerédi regularity lemma
=== Order theory === Higman's lemma Ultrafilter lemma
== Dynamical systems == Barbalat's lemma Kac's lemma (ergodic theory)
== Geometry == Shadowing lemma Big-little-big lemma (mathematics of paper folding) Gordan's lemma Hilbert's lemma
=== Euclidean geometry === Archimedes's lemmas Johnson–Lindenstrauss lemma (Euclidean geometry)
=== Hyperbolic geometry === Margulis lemma
=== Metric spaces === Lebesgue's number lemma (dimension theory)
=== Riemannian geometry === Gauss's lemma (Riemannian geometry)
== Mathematical logic == Craig interpolation lemma Diagonal lemma Lindenbaum's lemma Mostowski collapse lemma Teichmüller–Tukey lemma also known as Tukey's lemma Zorn's lemma; equivalent to the axiom of choice
=== Set theory ===
Covering lemma Delta lemma Dynkin lemma Fodor's lemma Fixed-point lemma for normal functions (axiomatic set theory) Moschovakis coding lemma Rasiowa–Sikorski lemma
== Number theory ==
Bézout's lemma Dwork's lemma Euclid's lemma Gauss's lemma Hensel's lemma Zolotarev's lemma Siegel's lemma (Diophantine approximation)
=== Analytic number theory === Hua's lemma Vaughan's lemma
=== Diophantine equations === Bhaskara's lemma
=== Sieve theory === Fundamental lemma of sieve theory
== Probability theory == Borel–Cantelli lemma Doob–Dynkin lemma Itô's lemma (stochastic calculus) Lovász local lemma Stein's lemma Wald's lemma
=== Statistics === Glivenko–Cantelli lemma Neyman–Pearson lemma Robbins lemma
=== Measure theory === Factorization lemma Fatou's lemma Frostman's lemma (geometric measure theory) Malliavin's absolute continuity lemma
== Topology == Lindelöf's lemma Urysohn's lemma Tube lemma
=== Differential topology === Morse lemma
=== Fixed-point theory ===
Knaster–Kuratowski–Mazurkiewicz lemma
=== Geometric topology === Dehn's lemma
=== Topological groups and semigroups === Ellis–Numakura lemma (topological semigroups)