List of lemmas

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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[edit]

Algebraic geometry[edit]

Category theory[edit]

A commutative diagram that illustrates the five lemma

Linear algebra[edit]

Group theory[edit]

Polynomials[edit]

Ring theory and commutative algebra[edit]

Universal algebra[edit]

Analysis[edit]

Complex analysis[edit]

Fourier analysis[edit]

Differential equations[edit]

Differential forms[edit]

Functional analysis[edit]

Mathematical series[edit]

Numerical analysis[edit]

Applied mathematics[edit]

diagram of a length-8 fast Fourier transform
diagram of a length-8 fast Fourier transform

Control theory[edit]

Computational complexity theory[edit]

Cryptography[edit]

Formal languages[edit]

Microeconomics[edit]

Combinatorics[edit]

Graph theory[edit]

Order theory[edit]

Dynamical systems[edit]

Geometry[edit]

Euclidean geometry[edit]

Hyperbolic geometry[edit]

Metric spaces[edit]

Riemannian geometry[edit]

Mathematical logic[edit]

Set theory[edit]

Number theory[edit]

Analytic number theory[edit]

Diophantine equations[edit]

Sieve theory[edit]

Probability theory[edit]

Statistics[edit]

Measure theory[edit]

Topology[edit]

Differential topology[edit]

Fixed-point theory[edit]

An example of a covering described by the Knaster–Kuratowski–Mazurkiewicz lemma

Geometric topology[edit]

Topological groups and semigroups[edit]