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Conversely, if X is a Hausdorff space and ker f is a closed set, then the coimage of f, if given the quotient space topology, must also be a Hausdorff space.

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## Some Related Sentences

Conversely and if

__Conversely__

**,**

__if__statistics were uncovered which contradicted

**a**cherished theory

**,**

**the**sources were denounced as faulty

**.**

__Conversely__

**,**experimenters would consider as impressive such statements as

**the**following

**,**which

**,**

__if__they turned out to

**be**hits

**,**are so unusual as to

**be**really significant:

__Conversely__

**,**

__if__he gives

**a**heavy rating to his own reading

**,**

**and**finds more accurate facts in it than in

**the**others

**,**

**a**point

**is**chalked up for

**the**intrinsic

**,**objective meaningfulness

**of**this type

**of**mediumistic material

**.**

__Conversely__

**,**

**a**subset R defines

**a**binary function

__if__

**and**only

__if__

**,**for any x in

**X**

**and**y in Y

**,**there exists

**a**unique z in Z such that ( x

**,**y

**,**z ) belongs to R

**.**

__Conversely__

**,**

__if__

**a**Boolean ring A

**is**

**given**

**,**we can turn it into

**a**Boolean algebra by defining x ∨ y := x + y + ( x · y )

**and**x ∧ y := x · y

**.**

__Conversely__

**,**

__if__

**the**second theory

**is**correct

**,**

**then**

**the**Athenians were merely reacting to

**the**Persians attacking them

**.**

__Conversely__

**the**equilibrium position

**is**said to

**be**" far to

**the**left "

__if__hardly any product

**is**formed from

**the**reactants

**.**

__Conversely__

**,**

__if__ƒ: C → C

**is**

**a**function which

**is**differentiable when regarded as

**a**function on R < sup > 2 </ sup >,

**then**ƒ

**is**complex differentiable

__if__

**and**only

__if__

**the**Cauchy – Riemann equations hold

**.**

__Conversely__

**,**

__if__

**the**amount

**of**fat

**is**increased

**,**increasing

**the**number

**of**calories ingested will only add weight

**.**

__Conversely__

**,**

__if__

**the**source

**of**waves

**is**moving away from

**the**observer

**,**each wave

**is**emitted from

**a**position farther from

**the**observer than

**the**previous wave

**,**so

**the**arrival time between successive waves

**is**increased

**,**reducing

**the**frequency

**.**

__Conversely__every partition

**of**comes from an equivalence relation in this way

**,**according to which

__if__

**and**only

__if__

**and**belong to

**the**same

**set**

**of**

**the**partition

**.**

If neither A nor B includes

**the**idea**of**existence**,****then**" some A are B " simply adjoins A to B**.**__Conversely__**,**__if__A or B do include**the**idea**of**existence in**the**way that " triangle " contains**the**idea " three angles equal to two right angles ",**then**" A exists "**is**automatically true**,****and**we have an ontological proof**of**A's existence**.**__Conversely__

**,**

__if__

**the**measured potential

**is**negative

**,**

**the**electrode

**is**more oxidizing than

**the**SHE ( such as Zn in ZnSO < sub > 4 </ sub > where

**the**standard electrode potential

**is**− 0

**.**76 V ).

__Conversely__

**,**

__if__

**the**firm

**is**able to get bulk discounts

**of**an input

**,**

**then**it could have economies

**of**scale in some range

**of**output levels even

__if__it has decreasing returns in production in that output range

**.**

__Conversely__

**,**daylight stock shot in daylight will look normal

**,**but orange

__if__shot under tungsten lights

**.**

__Conversely__

**,**

__if__

**the**data are sparse — that

**is**

**,**

__if__only K out

**of**N Fourier coefficients are nonzero —

**then**

**the**complexity can

**be**reduced to O ( K log N log ( N / K )),

**and**this has been demonstrated to lead to practical speedups compared to an ordinary FFT for N / K > 32 in

**a**large-N example ( N = 2 < sup > 22 </ sup >) using

**a**probabilistic approximate algorithm ( which estimates

**the**largest K coefficients to several decimal places ).

Conversely and X

__Conversely__

**,**British English favours fitted as

**the**past tense

**of**fit generally

**,**whereas

**the**preference

**of**American English

**is**more complex: AmEng prefers fitted for

**the**metaphorical sense

**of**having made an object " fit " ( i

**.**e., suited ) for

**a**purpose ; in spatial transitive contexts

**,**AmEng uses fitted for

**the**sense

**of**having made an object conform to an unchanged object that it surrounds ( e

**.**g., " fitted

__X__around Y ") but fit for

**the**sense

**of**having made an object conform to an unchanged object that surrounds it ( e

**.**g., " fit

__X__into Y ");

**and**for

**the**spatial senses ( both intransitive

**and**transitive )

**of**having been matching with respect to contour

**,**with no alteration

**of**either object implied

**,**AmEng prefers fit (" The clothes fit

**.**

That

**is****,****the**motivational internalist believes that there**is**an internal**,**necessary connection between one's conviction that__X__ought to**be**done**and**one's motivation to do__X__**.**__Conversely__**,****the**motivational externalist ( or moral externalist ) claims that there**is**no necessary**,**internal connection between moral convictions**and**moral motives**.**
Each convex

**set**containing__X__**must**( by**the**assumption that it**is**convex ) contain all convex combinations**of**points in__X__**,**so**the****set****of**all convex combinations**is**contained in**the**intersection**of**all convex sets containing__X__**.**__Conversely__**,****the****set****of**all convex combinations**is**itself**a**convex**set**containing__X__**,**so it**also**contains**the**intersection**of**all convex sets containing__X__**,****and**therefore**the**sets**given**by these two definitions**must****be**equal**.**
We define Thm ( C ) to

**be****the****set****of**all formulas that are valid in C**.**__Conversely__**,****if**__X__**is****a****set****of**formulas**,**let Mod (__X__)**be****the**class**of**all frames which validate every formula from__X__**.**
)

__Conversely__**,****if**B satisfies both**of****the**conditions 1**and**2**,****then**there**is****a**unique**topology**on__X__for which B**is****a**base ; it**is**called**the****topology**generated by B**.**__Conversely__

**,**

**if**R

**is**

**a**symmetric relation over

**a**

**set**

__X__

**,**one can interpret it as describing an undirected graph with

**the**elements

**of**

__X__as

**the**vertices

**and**

**the**pairs in R as

**the**edges

**.**

A hypergraph H may

**be**represented by**a**bipartite graph BG as follows:**the**sets__X__**and**E are**the**partitions**of**BG**,****and**( x < sub > 1 </ sub >, e < sub > 1 </ sub >) are connected with an edge**if****and**only**if**vertex x < sub > 1 </ sub >**is**contained in edge e < sub > 1 </ sub > in H**.**__Conversely__**,**any bipartite graph with fixed parts**and**no unconnected nodes in**the**second part represents some hypergraph in**the**manner described above**.**
for some real-valued functions

**a****and**b depending**,**respectively**,**on x**and**y**.**__Conversely__**,****given**any such pair**of**real-valued functions**,**there exists**a**vector field__X__satisfying 1**.****and**2**.**__Conversely__

**,**

**if**

__X__

**is**projective

**,**

**then**

**the**pullback

**of**under

**the**

**closed**immersion

**of**

__X__into

**a**projective

**space**

**is**very ample

**.**

__Conversely__

**,**

**a**complete variety

**is**close to being

**a**projective variety: Chow's lemma states that

**if**

__X__

**is**

**a**complete variety

**,**there

**is**

**a**projective variety Z

**and**

**a**birational morphism Z →

__X__

**.**

Conversely and is

__Conversely__

**,**an adiabatic process that

__is__irreversible

**and**extracts no work

__is__in an isenthalpic process

**,**such as viscous drag

**,**progressing towards

**a**nonnegative change in entropy

**.**

__Conversely__

**the**use

**of**true brass seems to have declined in Western Europe during this period in favour

**of**gunmetals

**and**other mixed alloys but by

**the**end

**of**

**the**first Millennium AD brass artefacts are found in Scandinavian graves in Scotland

**,**brass was being used in

**the**manufacture

**of**coins in Northumbria

**and**there

__is__archaeological

**and**historical evidence for

**the**production

**of**brass in Germany

**and**The Low Countries areas rich in calamine ore which would remain important centres

**of**brass making throughout

**the**medieval period

**,**especially Dinant – brass objects are still collectively known as dinanterie in French

**.**

__Conversely__

**,**because

**space**

__is__expanding

**,**

**and**more distant objects are receding ever more quickly

**,**light emitted by us today may never " catch up " to very distant objects

**.**

__Conversely__

**,**modern biological sciences ( including even concepts such as molecular ecology ) are intimately entwined

**and**dependent on

**the**methods developed through biotechnology

**and**what

__is__commonly thought

**of**as

**the**life sciences industry

**.**

__Conversely__

**,**

**the**islands do not receive

**the**upwellings ( cold streams ) that affect

**the**West African coast

**,**so

**the**air temperature

__is__cooler than in Senegal

**,**but

**the**sea

__is__actually warmer

**,**because

**the**orographic relief

**of**some islands

**,**as Sao Miguel with steep mountains

**,**cover it with rich woods

**and**luxuriant vegetation where

**the**dense moisture condense

**and**soak

**the**plants

**,**rocks

**,**soil

**,**logs

**,**moss etc

**.**

__Conversely__in francophone Canada

**,**one hundredth

**of**

**a**Canadian dollar

__is__informally called

**a**sou ( penny ), though cent

__is__official in both English

**and**French

**.**

__Conversely__

**,**an absence

**of**secure cycle-parking

__is__

**a**recurring complaint by cyclists from cities with low modal share

**of**cycling

**.**

* The spectrum

**of**any bounded linear operator on**a**Banach**space**__is__**a**nonempty compact subset**of****the**complex numbers C**.**__Conversely__**,**any compact subset**of**C arises in this manner**,**as**the**spectrum**of**some bounded linear operator**.**0.105 seconds.