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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 ).

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## Some Related Sentences

Every and mapping

__Every__singleton

**is**

**a**terminal object

**,**with

**the**functions

__mapping__all elements of

**the**source sets to

**the**single target element as morphisms.

__Every__finite group

**is**

**a**subgroup of

**the**

__mapping__class group of

**a**closed

**,**orientable surface

**,**moreover one can realize any finite group as

**the**group of isometries of some compact Riemann surface.

__Every__year

**,**

**the**American Society

**for**Photogrammetry

**and**Remote Sensing

**(**ASPRS ) presents

**the**Talbert Abrams Award to

**a**person who makes an outstanding contribution to aerial photography

**and**

__mapping__.

__Every__measurable entity maps into

**a**cardinal

**function**but not every cardinal

**function**

**is**

**the**result of

**the**

__mapping__of

**a**measurable entity.

Every and is

__Every__legislator from Brasstown Bald to Folkston

__is__going to have his every vote subjected to

**the**closest scrutiny as

**a**test of his political allegiances

**,**not his convictions.

__Every__detail in his interpretation has been beautifully thought out

**,**

**and**of these I would especially cite

**the**delicious laendler touch

**the**pianist brings to

**the**fifth variation

**(**an obvious indication that he

__is__playing with Viennese musicians )

**,**

**and**

**the**gossamer shading throughout.

__Every__taxpayer

__is__well aware of

**the**vast size of our annual defense budget

**and**most of our readers also realize that

**a**large portion of these expenditures go

**for**military electronics.

__Every__few days

**,**in

**the**early morning

**,**as

**the**work progressed

**,**twenty men would appear to push it ahead

**and**to shift

**the**plank foundation that distributed its weight widely on

**the**Rotunda pavement

**,**supported as it

__is__by ancient brick vaulting.

__Every__dream

**,**

**and**this

__is__true of

**a**mental image of any type even though it may be readily interpreted into its equivalent of wakeful thought

**,**

__is__

**a**psychic phenomenon

**for**which

**no**explanation

__is__available.

__Every__library borrower

**,**or at least those whose taste goes beyond

**the**five-cent fiction rentals

**,**knows what it

__is__to hear

**the**librarian say apologetically

**,**`` I'm sorry

**,**but we don't have that book.

__Every__community

**,**if it

__is__alive has

**a**spirit

**,**

**and**that spirit

__is__

**the**center of its unity

**and**identity.

The restricted principle "

__Every__partially ordered set has**a**maximal totally ordered subset "__is__also equivalent to AC over ZF.__Every__natural-born citizen of

**a**foreign state who

__is__also an American citizen

**and**every natural-born American citizen who

__is__

**a**citizen of

**a**foreign land owes

**a**double allegiance

**,**one to

**the**United States

**,**

**and**one to his homeland

**(**in

**the**event of an immigrant becoming

**a**citizen of

**the**US ), or to his adopted land

**(**in

**the**event of an emigrant natural born citizen of

**the**US becoming

**a**citizen of another nation

**).**

__Every__line of written text

__is__

**a**mere reflection of references from any of

**a**multitude of traditions

**,**or

**,**as Barthes puts it

**,**"

**the**text

__is__

**a**tissue of quotations drawn from

**the**innumerable centres of culture "; it

__is__never original.

__Every__year

**,**on

**the**last Sunday in April

**,**there

__is__an ice fishing competition in

**the**frozen estuarine waters of

**the**Anadyr River's mouth.

__Every__lattice element of

**the**structure

__is__in its proper place

**,**whether it

__is__

**a**single atom or

**a**molecular grouping.

Every and Lipschitz

__Every__special

**uniformly**

**continuous**real-valued

**function**defined on

**the**metric space

**is**

**uniformly**approximable by means of

__Lipschitz__functions.

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__

__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__

__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.

__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 hence

*

__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__topological ring

**is**

**a**topological group

**(**with respect to addition )

**and**

__hence__

**a**uniform space in

**a**natural manner.

__Every__finite-dimensional normed space

**is**reflexive

**,**simply because in this case

**,**

**the**space

**,**its dual

**and**bidual all have

**the**same linear dimension

**,**

__hence__

**the**linear injection J from

**the**definition

**is**bijective

**,**by

**the**rank-nullity theorem.

__Every__Boolean algebra

**is**

**a**Heyting algebra when

**a**→ b

**is**defined as usual as ¬

**a**∨ b

**,**as

**is**every complete distributive lattice when

**a**→ b

**is**taken to be

**the**supremum of

**the**set of all c

**for**which

**a**∧ c ≤ b. The open sets of

**a**topological space form

**a**complete distributive lattice

**and**

__hence__

**a**Heyting algebra.

*

__Every__finite-dimensional simple algebra over C must be**a**matrix ring over C**and**__hence__every central simple algebra over C must be**a**matrix ring over C.
* T-carbon:

__Every__carbon atom in diamond**is**replaced with**a**carbon tetrahedron**(**__hence__' T-carbon ').__Every__year

**a**number of kloofers get injured or need rescue

**and**

__hence__kloofers need to take great care

**and**preferably be accompanied by an experienced kloofer.

*

__Every__substructure**is****the**union of its finitely generated substructures ;__hence__Sub**(**A )**is**an algebraic lattice.
#

__Every__plurality**,**being**a**combination of units**,**presupposes an original unity ;__hence__**,**even those that assume**a**plurality of gods must logically admit**the**prior existence of**a**Divine Unity —**a**Neoplatonic argument borrowed by Baḥya from**the**Brothers of Purity.
Contraries cannot both be true

**,**although they can both be false**,****and**__hence__their contradictories are both true**(****for**example**,**both**,**'__Every__man**is**honest ,'**and**' No man**is**honest ,' are false.__Every__human mind inherits

**a**complement of species-specific “ elementary ideas ”

**(**Elementargedanken ),

**and**

__hence__

**the**minds of all people

**,**regardless of their race or culture

**,**operate in

**the**same way.

Previously

**a**daily segment**,**Underbelly didn't appear as often in**the**rotation**(**__hence__Maddow's inclination to add "__Every__day ... or so " to her introduction of**the**segment**).**
The Commission Report quotes Max Weber

**,**__Every__bureaucracy seeks to increase**the**superiority of**the**professionally informed by keeping their knowledge**and**intentions secret ... Bureaucracy naturally welcomes**a**poorly informed**and**__hence__**a**powerless parliament — at least insofar as ignorance somehow agrees with**the**bureaucracy ’ s interests.__Every__Friday night

**,**

**the**counselors organize " an event so fun that it

**is**necessary

**and**sufficient ,"

__hence__

**the**name " mandatory fun.

__Every__element x of G gives rise to

**a**tensor-preserving self-conjugate natural transformation via multiplication by x on each representation

**,**

**and**

__hence__one has

**a**map.

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