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** The Baire category theorem about complete metric spaces, and its consequences, such as the open mapping theorem and the closed graph theorem.
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** and Baire
** 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
** 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 ).
** 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.
** and theorem
** 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.
** 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.
** 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.
** 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.
** Artin reciprocity law, a general theorem in number theory that provided a partial solution to Hilbert's ninth problem
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