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* Every arithmetical subset of Cantor space of < sup >( or?

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## Some Related Sentences

Every and arithmetical

__Every__

__arithmetical__set is implicitly

__arithmetical__; if X is arithmetically defined by φ ( n ) then it is implicitly defined by the formula

Every and subset

__Every__such

__subset__has a smallest element, so to specify our choice function we can simply say that it maps each set to the least element

**of**that set.

** 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.
The restricted principle "

__Every__partially ordered set has a maximal totally ordered__subset__" is also equivalent to AC over ZF.__Every__

__subset__A

**of**the vector

**space**is contained within a smallest convex set ( called the convex hull

**of**A ), namely the intersection

**of**all convex sets containing A.

*****

__Every__separable metric

**space**is isometric to a

__subset__

**of**the ( non-separable ) Banach

**space**l

**<**

**sup**>∞</

**sup**>

**of**all bounded real sequences with the supremum norm ; this is known as the Fréchet embedding.

*****

__Every__separable metric

**space**is isometric to a

__subset__

**of**C (), the separable Banach

**space**

**of**continuous functions → R, with the supremum norm.

__Every__element s, except a possible greatest element, has a unique successor ( next element ), namely the least element

**of**the

__subset__

**of**all elements greater than s.

__Every__

__subset__which has an upper bound has a least upper bound.

__Every__

__subset__

**of**a nowhere dense set is nowhere dense, and the union

**of**finitely many nowhere dense sets is nowhere dense.

__Every__

__subset__

**of**the Hilbert cube inherits from the Hilbert cube the properties

**of**being both metrizable ( and therefore T4 ) and second countable.

It is more interesting that the converse also holds:

__Every__second countable T4**space**is homeomorphic to a__subset__**of**the Hilbert cube.*****

__Every__totally disconnected compact metric

**space**is homeomorphic to a

__subset__

**of**a countable product

**of**discrete spaces.

*****

__Every__irreducible closed

__subset__

**of**P

**<**

**sup**> n </

**sup**

**>(**k )

**of**codimension one is a hypersurface ; i. e., the zero set

**of**some homogeneous polynomial.

Every and Cantor

__Cantor__points out that his constructions prove more — namely, they provide a new proof

**of**Liouville's theorem:

__Every__interval contains infinitely many transcendental numbers.

Every and space

__Every__Hilbert

__space__X is a Banach

__space__because, by definition, a Hilbert

__space__is complete with respect to the norm associated with its inner product, where a norm and an inner product are said to be associated if for all x ∈ X.

*****

__Every__topological

__space__X is a dense subspace

**of**a compact

__space__having at most one point more than X, by the Alexandroff one-point compactification.

*****

__Every__continuous map from a compact

__space__to a Hausdorff

__space__is closed and proper ( i. e., the pre-image

**of**a compact set is compact.

__Every__node on the Freenet network contributes storage

__space__to hold files, and bandwidth that it uses to route requests from its peers.

*****

__Every__Lie group is parallelizable, and hence an orientable manifold ( there is a bundle isomorphism between its tangent bundle and the product

**of**itself with the tangent

__space__at the identity )

__Every__vector

__space__has a basis, and all bases

**of**a vector

__space__have the same number

**of**elements, called the dimension

**of**the vector

__space__.

__Every__normed vector

__space__V sits as a dense subspace inside a Banach

__space__; this Banach

__space__is essentially uniquely defined by V and is called the completion

**of**V.

Every and <

*****

__Every__quadratic Bézier curve is also a cubic Bézier curve, and more generally, every degree n Bézier curve is also a degree m curve for any m > n. In detail, a degree n curve with control points P

__<__sub > 0 </ sub >, …, P

__<__sub > n </ sub > is equivalent ( including the parametrization ) to the degree n + 1 curve with control points P '< sub > 0 </ sub >, …, P '< sub > n + 1 </ sub >, where.

__Every__bijective function g has an inverse g

__<__

**sup**>− 1 </

**sup**>, such that gg

__<__

**sup**>− 1 </

**sup**> = I ;

__Every__holomorphic function can be separated into its real and imaginary parts, and each

**of**these is a solution

**of**Laplace's equation on R

__<__

**sup**> 2 </

**sup**>.

__Every__atom across this plane has an individual set

**of**emission cones .</ p >

__<__p > Drawing the billions

**of**overlapping cones is impossible, so this is a simplified diagram showing the extents

**of**all the emission cones combined.

__Every__time an MTA receives an email message, it adds a

__<__tt > Received </ tt > trace header field to the top

**of**the header

**of**the message, thereby building a sequential record

**of**MTAs handling the message.

__Every__binary relation R on a set S can be extended to a preorder on S by taking the transitive closure and reflexive closure, R

__<__

**sup**>+=</

**sup**>.

__Every__twin prime pair except ( 3, 5 ) is

**of**the form ( 6n − 1, 6n + 1 ) for some natural number n, and with the exception

**of**

__<__var > n </ var > = 1,

__<__var > n </ var > must end in 0, 2, 3, 5, 7,

**or**8.

__Every__random vector gives rise to a probability measure on R

__<__

**sup**> n </

**sup**> with the Borel algebra as the underlying sigma-algebra.

*****

__Every__linear combination

**of**its components Y = a

__<__sub > 1 </ sub > X

__<__sub > 1 </ sub > + … + a

__<__sub > k </ sub > X

__<__sub > k </ sub > is normally distributed.

__Every__sedenion is a real linear combination

**of**the unit sedenions 1,

__<__var > e </ var >< sub > 1 </ sub >,

__<__var > e </ var >< sub > 2 </ sub >,

__<__var > e </ var >< sub > 3 </ sub >, ..., and

__<__var > e </ var >< sub > 15 </ sub >,

__Every__prime ideal P in a Boolean ring R is maximal: the quotient ring R / P is an integral domain and also a Boolean ring, so it is isomorphic to the field F

__<__sub > 2 </ sub >, which shows the maximality

**of**P. Since maximal ideals are always prime, prime ideals and maximal ideals coincide in Boolean rings.

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