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Every Riemann surface is a two-dimensional real analytic manifold ( i. e., a surface ), but it contains more structure ( specifically a complex structure ) which is needed for the unambiguous definition of holomorphic functions.

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## Some Related Sentences

Every and Riemann

__Every__

__Riemann__

**surface**

**is**

**the**quotient

**of**

**a**free, proper and

**holomorphic**action

**of**

**a**discrete group on its universal covering and this universal covering

**is**holomorphically isomorphic

**(**one also says: " conformally equivalent ") to one

**of**

**the**following:

#

__Every__Riemannian metric on**a**__Riemann__**surface****is**Kähler, since**the**condition**for**ω to be closed**is**trivial in 2**(****real****)**dimensions**.**__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__time we are computing

**a**

__Riemann__sum, we are using

**a**particular instantiation

**of**

**the**integrator

**.**

Every and surface

__Every__form

**is**

**the**delimitation

**of**

**a**

__surface__by another one ;

**it**possesses an inner content,

**the**effect

**it**produces on one who looks at

**it**attentively

**.**

__Every__aspect

**of**

**the**store

**is**mapped out and attention

**is**paid to colour, wording and even

__surface__texture

**.**

__Every__antiseptic, however good,

**is**

**more**or less toxic and irritating to

**a**wounded

__surface__; as

**a**result, in surgery,

**the**antiseptic method has been replaced by aseptic method,

**which**

**is**preventative in nature and relies on keeping free from

**the**invasion

**of**bacteria rather than destroying them when present

**.**

__Every__now and then,

**the**

__surface__water sloshes back across

**the**ocean, bringing warm water temperatures along

**the**eastern coasts

**of**

**the**pacific

**.**

__Every__such black body emits from its

__surface__with

**a**spectral radiance that Kirchhoff labeled

**(**

**for**specific intensity,

**the**traditional name

**for**spectral radiance ).

__Every__17 years, Brood X cicadas tunnel en masse to

**the**

__surface__

**of**

**the**ground, lay eggs, and then die off in several weeks

**.**

__Every__minimal projective ruled

__surface__other than

**the**projective plane

**is**

**the**projective bundle

**of**

**a**2-dimensional vector bundle over some curve

**.**

__Every__vehicle function that changes direction or speed relies on friction between

**the**tires and

**the**road

__surface__

**.**

__Every__single object or point

**is**dwarfed ;

**the**valley

**of**

**the**Hudson

**is**only

**a**wrinkle in

**the**earth's

__surface__

**.**

__Every__

__surface__

**of**

**the**vaulted ceiling

**is**occupied with preserved fishes, stuffed mammals and curious shells, with

**a**stuffed crocodile suspended in

**the**centre

**.**

__Every__integer 2g ' 2g matrix with < sup >*</ sup > arises as

**the**Seifert matrix

**of**

**a**knot with genus g Seifert

__surface__

**.**

__Every__morning before sunrise,

**the**floor

**of**

**the**owners house, or where ever

**it**may be,

**is**cleaned with water and

**the**muddy floor

**is**swept well

**for**an even

__surface__

**.**

According to Dale E

**.**Dawkins, AMC's vice-president, "__Every__square inch**of**inner__surface__on exterior body panels**is**galvanized on our Spirit, Concord, and Eagle models**.**__Every__particular finite line,

__surface__, or solid

**which**may possibly be

**the**object

**of**our thought

**is**an idea existing only in

**the**mind, and consequently each part

**of**

**it**must be perceived

**.**

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

**.**

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