** Every infinite game in which is a Borel subset of Baire space is determined.

** Category ( topology ) in the context of Baire spaces

** In the category of Riemann surfaces, an automorphism is a bijective biholomorphic map ( also called a conformal map ), from a surface to itself.

** Systems Biology comes under this category including reaction fluxes and variable concentrations of metabolites

** Dual ( category theory ), a formalization of mathematical duality

** Concept learning is the induction of a concept ( category ) from observations

** Inform category: A Change in the Weather by Andrew Plotkin

** TADS category: Uncle Zebulon's Will by Magnus Olsson

** Limit ( category theory )

** Chamois leather also falls into the category of aldehyde tanning and like brain tanning produces a highly water absorbent leather.

** the materials are subject to a subpoena-although many practitioners regard that fact as a category of permissible disclosure, not as a categorical exclusion from confidentiality ( because court-ordered secrecy provisions may apply even in case of a subpoena ).

** the product category, a category that is the product of categories.

** A devastating category 4 Cyclone strikes Andhra Pradesh, India.

** Hondo-Louis L ' Amour ( Note: Originally announced on February 15, 1954 as a nominee in this category.

** Poultry – category of domesticated birds kept by humans for the purpose of collecting their eggs, or killing for their meat and / or feathers.

** the category of vector spaces over a field K.

** the category of vector spaces over a field K.

** Set, the category of sets

** Top, the category of topological spaces

** Grp, the category of groups

** Ab, the category of abelian groups

** Ring, the category of rings

** K-Vect, the category of vector spaces over a field K

** R-Mod, the category of modules over a commutative ring R

** CmptH, the category of all compact Hausdorff spaces

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

** 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.