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Every continuous function in the function space can be represented as a linear combination of basis functions, just as every vector in a vector space can be represented as a linear combination of basis vectors.

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## Some Related Sentences

Every and continuous

*

__Every____continuous__functor on**a**small-complete category which satisfies**the**appropriate solution set condition has**a**left-adjoint (**the**Freyd adjoint functor theorem ).__Every__character is automatically

__continuous__from A to C

**,**since

**the**kernel

**of**

**a**character is

**a**maximal ideal

**,**which is closed

**.**

*

__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__contraction mapping is Lipschitz

__continuous__and hence uniformly

__continuous__( for

**a**Lipschitz

__continuous__

**function**

**,**

**the**constant k is no longer necessarily less than 1 ).

__Every__

__continuous__map f: X → Y induces an algebra homomorphism C ( f ): C ( Y ) → C ( X ) by

**the**rule C ( f )( φ ) = φ o f for

**every**φ

**in**C ( Y ).

*

__Every__separable metric**space**is isometric to**a**subset**of**C (),**the**separable Banach**space****of**__continuous__**functions**→ R**,**with**the**supremum norm**.**__Every__topological group

**can**

**be**viewed

**as**

**a**uniform

**space**

**in**two ways ;

**the**left uniformity turns all left multiplications into uniformly

__continuous__maps while

**the**right uniformity turns all right multiplications into uniformly

__continuous__maps

**.**

__Every__map that is injective

**,**

__continuous__and either open or closed is an embedding ; however there are also embeddings which are neither open nor closed

**.**

*

__Every__compact Hausdorff**space****of**weight at most ( see Aleph number ) is**the**__continuous__image**of**( this does not need**the**continuum hypothesis**,**but is less interesting**in**its absence ).__Every__place south

**of**

**the**Antarctic Circle experiences

**a**period

**of**twenty-four hours '

__continuous__daylight at least once per year

**,**and

**a**period

**of**twenty-four hours '

__continuous__night time at least once per year

**.**

Every and function

__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

**.**

__Every__effectively calculable

__function__( effectively decidable predicate ) is general recursive italics

__Every__bijective

__function__g has an inverse g < sup >− 1 </ sup >, such that gg < sup >− 1 </ sup > = I ;

__Every__entire

__function__

**can**

**be**

**represented**

**as**

**a**power series that converges uniformly on compact sets

**.**

__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__completely multiplicative

__function__is

**a**homomorphism

**of**monoids and is completely determined by its restriction to

**the**prime numbers

**.**

__Every__time another object or customer enters

**the**line to wait

**,**they join

**the**end

**of**

**the**line and represent

**the**“ enqueue ”

__function__

**.**

__Every__type that is

**a**member

**of**

**the**type class defines

**a**

__function__that will extract

**the**data from

**the**string representation

**of**

**the**dumped data

**.**

__Every__output

**of**an encoder

**can**

**be**described by its own transfer

__function__

**,**which is closely related to

**the**generator polynomial

**.**

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__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__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

**.**

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