** Euclidean groups

** Euclidean domain, an integral domain which allows a suitable generalization of the Euclidean algorithm

** 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.

** Euclidean space, which is flat, is a simple example of Ricci-flat, hence Einstein metric.

** Moreover, W = 0 if and only if the metric is locally conformal to the standard Euclidean metric ( equal to fg, where g is the standard metric in some coordinate frame and f is some scalar function ).

** Differential topology, in multivariable calculus, the differential of a smooth map between Euclidean spaces or differentiable manifolds is the approximating linear map between the tangent spaces, called pushforward ( differential )

** triangulation ( geometry ), division of the Euclidean plane into triangles and of Euclidean spaces into simplices

** Exotic R < sup > 4 </ sup >-differentiable manifold homeomorphic but not diffeomorphic to the Euclidean space R < sup > 4 </ sup >

** yields and the Euclidean division stops.

** Every vector space has a basis.

** The closed unit ball of the dual of a normed vector space over the reals has an extreme point.

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

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

** On every infinite-dimensional topological vector space there is a discontinuous linear map.

** A uniform space is compact if and only if it is complete and totally bounded.

** Every Tychonoff space has a Stone – Čech compactification.

** In topology, morphisms between topological spaces are called continuous maps, and an automorphism of a topological space is a homeomorphism of the space to itself, or self-homeomorphism ( see homeomorphism group ).

** 8-bit CPU, 16-bit address space

** Ariane ( rocket family ), a series of space vehicles

** Many embedded applications have a limited amount of physical space for circuitry ; keeping peripherals on-chip will reduce the space required for the circuit board.

** Social Security number with no dashes or spaces followed immediately by " USN ", space, blood group

** Stave-core-Consists of wooden slats stacked upon one another in a manner similar to a plank & batten door ( though the slats are usually thinner ) or the wooden-block hollow-core ( except that the space is entirely filled ).

** Solid-core-Can consist of low-density particle board or foam used to completely fill the space within the door.

** Stave-core-Consists of wooden slats stacked upon one another in a manner similar to a plank & batten door ( though the slats are usually thinner ) or the wooden-block hollow-core ( except that the space is entirely filled ).

** Solid-core-Can consist of low-density particle board or foam used to completely fill the space within the door.

** Three-dimensional space of action ( 4 %) — Is the cut true to the physical / spatial relationships within the diegesis?

** In statistics, it is used as the symbol for the sample space, or total set of possible outcomes.

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

** Garden square, an open space with buildings surrounding a garden

** Address space

** Virtual address space

A space X can be embedded into the double dual X ** by

** 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.

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

** 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.

** Hausdorff maximal principle: In any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset.

** For every non-empty set S there is a binary operation defined on S that makes it a group.

** 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.

** If the set A is infinite, then there exists an injection from the natural numbers N to A ( see Dedekind infinite ).

** 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.

** The Lebesgue measure of a countable disjoint union of measurable sets is equal to the sum of the measures of the individual sets.

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