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Every Möbius transformation is a bijective conformal map of the Riemann sphere to itself.

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## Some Related Sentences

Every and transformation

__Every__element in O ( 1, 3 ) can be written as

**the**semidirect product

**of**

**a**proper, orthochronous

__transformation__and an element

**of**

**the**discrete group

__Every__universal cover p: D → X

**is**regular, with deck

__transformation__group being isomorphic

**to**

**the**fundamental group

**.**

__Every__bounded linear

__transformation__from

**a**normed vector space

**to**

**a**complete, normed vector space can be uniquely extended

**to**

**a**bounded linear

__transformation__from

**the**completion

**of**

**to**

**.**

__Every__six rounds,

**a**logical

__transformation__layer

**is**applied:

**the**so-called " FL-function " or its inverse

**.**

__Every__orthogonal

__transformation__

**of**

**a**k-frame in R < sup > n </ sup > results in another k-frame, and any two k-frames are related by some orthogonal

__transformation__

**.**

__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**

**.**

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 bijective

__Every__

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

__Every__inner automorphism

**is**indeed an automorphism

**of**

**the**group G, i

**.**e

**.**it

**is**

**a**

__bijective__

**map**from G

**to**G and it

**is**

**a**homomorphism ; meaning ( xy )< sup >

**a**</ sup >

__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__finite-dimensional Hausdorff topological vector space

**is**reflexive, because J

**is**

__bijective__by linear algebra, and because there

**is**

**a**unique Hausdorff vector space topology on

**a**finite dimensional vector space

**.**

Every and map

*

__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__vector v in determines

**a**linear

__map__from R

**to**taking 1

**to**v, which can be thought

**of**as

**a**Lie algebra homomorphism

**.**

__Every__smooth ( or differentiable )

__map__φ: M → N between smooth ( or differentiable ) manifolds induces natural linear maps between

**the**corresponding tangent spaces:

__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__algebraic curve C

**of**genus g ≥ 1

**is**associated with an abelian variety J

**of**dimension g, by means

**of**an analytic

__map__

**of**C into J

**.**

__Every__covering

__map__

**is**

**a**semicovering, but semicoverings satisfy

**the**" 2 out

**of**3 " rule: given

**a**composition

**of**maps

**of**spaces, if two

**of**

**the**maps are semicoverings, then so also

**is**

**the**third

**.**

*

__Every__bundle**of**Lie algebras over**a**smooth manifold defines**a**Lie algebroid where**the**Lie bracket**is**defined pointwise and**the**anchor__map__**is**equal**to**zero**.**
* The embedding theorem for Stein manifolds states

**the**following:__Every__Stein manifold**of**complex dimension can be embedded into by**a**biholomorphic proper__map__**.**__Every__issue

**of**our periodical will therefore include one or more

__map__supplements, and their design will guarantee

**a**continuous and easily accessible supplement in easy-to-manage form with special regard for those who own Stielers Hand-Atlas, Berghaus ’ s Physical Atlas, and other

__map__publications

**of**

**the**( Perthes ) Institute

**.**

__Every__summer,

**the**town prepares for

**the**one-week summer festival, " Finnsnes i Fest ", aiming

**to**put Finnsnes on

**the**

__map__

**.**

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