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Page "Axiom of choice" ¶ 98
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** and Baire
** Every infinite game in which is a Borel subset of Baire space is determined.
** Category ( topology ) in the context of Baire spaces

** and category
** 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

** and theorem
** 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.

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