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* 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.

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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__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__

__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 map

__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__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__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__

**.**

__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 from

__Every__morning early, in

**the**summer, we searched

**the**trunks

**of**

**the**trees as high as we could reach for

**the**locust shells, carefully detached their hooked claws

__from__

**the**bark where they hung,

**and**stabled them,

**a**weird faery herd, in an angle between

**the**high roots

**of**

**the**tulip tree, where no grass grew in

**the**dense shade

**.**

__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__pitch in

**the**game brought forth

**a**howl

__from__

**the**enraptured audience

**and**every fly ball

**the**visitors dropped

**(**

**and**because their right fielder was still

**a**little fuzzy

__from__drink, they dropped many ) called forth yelps

**of**derision

**.**

__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__book followed

**a**different train

**of**thought,

__from__inspiration

**to**solution, according

**to**her autobiography

**.**

__Every__time

**a**speech sound

**is**produced for

**a**given phoneme, it will be slightly different

__from__other utterances, even for

**the**same speaker

**.**

__Every__year both clubs play

**the**" Klassieker " (" The Classic "),

**a**derby match between

**the**teams

__from__

**the**two largest cities

**of**

**the**Netherlands

**.**

Four other hits

__from__**the**album made**the**Pop top 20: "__Every__Heartbeat "**(**No**.**2 ), " That's What Love Is For "**(**No**.**7 ), " Good For Me "**(**No**.**8 ),**and**" I Will Remember You "**(**No**.**20 ).*****Revised Code

**of**Washington 9

**.**12

**.**010: "

__Every__person who brings on his or her own behalf, or instigates, incites, or encourages another

**to**bring, any false suit at law or in equity in any court

**of**this state, with intent thereby

**to**distress or harass

**a**defendant in

**the**suit, or who serves or sends any paper or document purporting

**to**be or resembling

**a**judicial process, that

**is**not in fact

**a**judicial process,

**is**guilty

**of**

**a**misdemeanor ;

**and**in case

**the**person offending

**is**an attorney, he or she may, in addition thereto be disbarred

__from__practicing law within this state

**.**

__Every__year,

**the**European Joint Conferences on Theory

**and**Practice

**of**Software

**(**ETAPS ) sponsors

**the**International Conference on Compiler Construction

**(**CC ), with papers

__from__both

**the**academic

**and**industrial sectors

**.**

__Every__Halloween, Dabney House conducts

**the**infamous " Millikan pumpkin-drop experiment "

__from__

**the**top

**of**Millikan Library,

**the**highest point on campus

**.**

__Every__argues that "

**the**disparagement

**of**myth in our own civilization " stems partly

__from__objections

**to**perceived idolatry, objections which intensified in

**the**Reformation, both among Protestants

**and**among Catholics reacting against

**the**classical mythology revived during

**the**Renaissance

**.**

__Every__gun that

**is**made, every warship launched, every rocket fired signifies, in

**the**final sense,

**a**theft

__from__those who hunger

**and**are not fed, those who are cold

**and**are not clothed

**.**

In Norse mythology, Draupnir

**(**Old Norse "**the**dripper ")**is****a**gold ring possessed by**the**god Odin with**the**ability**to**multiply itself:__Every__ninth night eight new rings ' drip '__from__Draupnir, each one**of****the**same size**and**weight as**the**original**.**__Every__time

**a**diode switches

__from__on

**to**off or vice versa,

**the**configuration

**of**

**the**linear network changes

**.**

*****

__Every__June, Ellensburg hosts Dachshunds on Parade, an event that draws Dachshund dog owners

__from__all over

**the**Northwest

**.**

For example

**the**words**of**" I'm**a**Man You Don't Meet__Every__Day "**(**Roud 975 ) are known__from__**a**broadside in**the**Bodleian Library**.**
Group actions / representations:

__Every__group G can be considered as**a**category with**a**single object whose morphisms are**the**elements**of**G**.**A functor__from__G**to**Set**is**then nothing but**a**group action**of**G on**a**particular**set**,**i****.****e****.****a**G-set**.**0.316 seconds.