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Page "Axiom of choice" ¶ 86
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** and Banach
** The Hahn Banach theorem in functional analysis, allowing the extension of linear functionals
** The Banach Alaoglu theorem about compactness of sets of functionals.
** Banach algebra: an associative algebra A over the real or complex numbers which at the same time is also a Banach space.
** c < sub > 0 </ sub >, the Banach space of real sequences that converge to zero

** and
** Atlas III was a US launch vehicle ( 2000 2005 )
** Atlas V ( 2002 Present )
** Atlas Major, a Standard Motor Company van 1962 1963
** The Nielsen Schreier theorem, that every subgroup of a free group is free.
** Every Tychonoff space has a Stone Čech compactification.
** This is a distinguished work which stands out from, and above, many of the books and articles which have ben written in this century on Avicenna ( Ibn Sīnā ) ( A. D. 980 1037 ).
** The numbers and are not algebraic numbers ( see the Lindemann Weierstrass theorem ); hence they are transcendental.
** Laozi ( 5th 4th century BC )
** Ge Hong ( 283 AD 343 AD )
** Xun Zi ( c. 312 BC 230 BC )
** Gongsun Long ( c. 325 BC c. 250 BC )
** Zou Yan ( 305 BC 240 BC )
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** Haliotis brazieri f. hargravesi ( Cox, 1869 ) synonym: Haliotis ethologus, the Mimic abalone, Haliotis hargravesi, the Hargraves ’ s abalone
** Haliotis dalli roberti McLean, 1970 synonym: Haliotis roberti
** Haliotis diversicolor squamata Reeve, 1846 synonym: Haliotis squamata the scaly Australian abalone
** Haliotis diversicolor supertexta the Taiwan abalone or jiukong
** Haliotis kamtschatkana assimilis Dall, 1878 synonym: Haliotis assimilis, the threaded abalone
** Haliotis ovina f. patamakanthini Dekker, Regter, & Gras, 2001 synonym: Haliotis patamakanthini
** Haliotis rubra conicopora Péron, 1816 synonym: Haliotis conicopora the conical pore abalone

** and Tarski
** Alfred Tarski, Polish logician and mathematician ( died 1983 )

** and paradox
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** Shaar HaYichud-The Gate of Unity, Dovber Schneuri-A detailed explanation of the paradox of divine simplicity.
** Heat death paradox, a philosophical examination of the cosmological event
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** and .
** Eunectes murinus, the green anaconda, the largest species, is found east of the Andes in Colombia, Venezuela, the Guianas, Ecuador, Peru, Bolivia, Brazil and on the island of Trinidad.
** Eunectes notaeus, the yellow anaconda, a smaller species, is found in eastern Bolivia, southern Brazil, Paraguay and northeastern Argentina.
** Eunectes deschauenseei, the dark-spotted anaconda, is a rare species found in northeastern Brazil and coastal French Guiana.
** Eunectes beniensis, the Bolivian anaconda, the most recently defined species, is found in the Departments of Beni and Pando in Bolivia.
** 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.
** Trichotomy: If two sets are given, then either they have the same cardinality, or one has a smaller cardinality than the other.
** The Cartesian product of any family of nonempty sets is nonempty.
** König's theorem: Colloquially, the sum of a sequence of cardinals is strictly less than the product of a sequence of larger cardinals.
** Every surjective function has a right inverse.
** Zorn's lemma: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.
** Hausdorff maximal principle: In any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset.
** Tukey's lemma: Every non-empty collection of finite character has a maximal element with respect to inclusion.
** Antichain principle: Every partially ordered set has a maximal antichain.
** Every vector space has a basis.
** Every unital ring other than the trivial ring contains a maximal ideal.
** For every non-empty set S there is a binary operation defined on S that makes it a group.
** The closed unit ball of the dual of a normed vector space over the reals has an extreme point.
** Tychonoff's theorem stating that every product of compact topological spaces is compact.
** In the product topology, the closure of a product of subsets is equal to the product of the closures.
** 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.
** Any union of countably many countable sets is itself countable.

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