** Gromov's compactness theorem ( topology ) in symplectic topology

** The Banach – Alaoglu theorem about compactness of sets of functionals.

** Well-ordering theorem: Every set can be well-ordered.

** Tarski's theorem: For every infinite set A, there is a bijective map between the sets A and A × A.

** König's theorem: Colloquially, the sum of a sequence of cardinals is strictly less than the product of a sequence of larger cardinals.

** Tychonoff's theorem stating that every product of compact topological spaces is compact.

** If S is a set of sentences of first-order logic and B is a consistent subset of S, then B is included in a set that is maximal among consistent subsets of S. The special case where S is the set of all first-order sentences in a given signature is weaker, equivalent to the Boolean prime ideal theorem ; see the section " Weaker forms " below.

** The Vitali theorem on the existence of non-measurable sets which states that there is a subset of the real numbers that is not Lebesgue measurable.

** Stone's representation theorem for Boolean algebras needs the Boolean prime ideal theorem.

** The Nielsen – Schreier theorem, that every subgroup of a free group is free.

** The Hahn – Banach theorem in functional analysis, allowing the extension of linear functionals

** The theorem that every Hilbert space has an orthonormal basis.

** The Baire category theorem about complete metric spaces, and its consequences, such as the open mapping theorem and the closed graph theorem.

** Gödel's completeness theorem for first-order logic: every consistent set of first-order sentences has a completion.

** The numbers and are not algebraic numbers ( see the Lindemann – Weierstrass theorem ); hence they are transcendental.

** Hilbert's basis theorem

** Bayes ' theorem

** More generally, Rademacher's theorem extends the differentiability result to Lipschitz mappings between Euclidean spaces: a Lipschitz map ƒ: U → R < sup > m </ sup >, where U is an open set in R < sup > n </ sup >, is almost everywhere differentiable.

** Lyapunov's central limit theorem

** Superposition theorem, in electronics

** " Kelvin's vorticity theorem for incompressible or barotropic flow ".

** Artin reciprocity law, a general theorem in number theory that provided a partial solution to Hilbert's ninth problem

** Various proofs of the four colour theorem.

** In metric geometry an automorphism is a self-isometry.

** Schwarzschild metric, a description of the geometry around a special type of black hole

** Origin ( mathematics ), a fixed point of reference for the geometry of the surrounding space

** Pole and polar line, a duality with respect to conics in projective geometry

** Theodosius of Bithynia, Greek astronomer and mathematician who will write the Sphaerics, a book on the geometry of the sphere ( d. c. 100 BC )

** History of Geometry, on the early history of Greek geometry ( several quotes survive )

** Torsion tensor in differential geometry

** Duality ( projective geometry ), general principle of projective geometry

** In elementary mathematics, especially elementary geometry:

** Parabolic geometry

** Projective geometry is a non-Euclidean geometry that involves projective spaces.

** Books by Hirschfeld on finite geometry

** Use of tap with improper tap geometry for a particular application.

** The geometry ( physical bounds ) of the problem is defined.

** Similarity ( geometry ) –

** Congruence ( geometry ) –

** Cartesian coordinate system, for representing position and other spatial concepts in analytic geometry

** Transverse leaf springs when used as a suspension link, or four quarter elliptics on one end of a car are similar to wishbones in geometry, but are more compliant.

** Focus ( geometry ), a special point used in describing conic sections

** Lune of Hippocrates, in geometry a plane region bounded by arcs of circles and amenable to quadrature

** List of combinatorial computational geometry topics

** List of computer graphics and descriptive geometry topics

** List of numerical computational geometry topics