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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.

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## Some Related Sentences

Conversely and subset

* 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**.**__Conversely__

**,**every Polish space is homeomorphic

**to**

**a**G < sub > δ </ sub >-

__subset__of the Hilbert cube

**.**

__Conversely__

**,**words

**such**as banjee

**,**while well-established

**in**

**a**

__subset__of gay society

**,**have never made the transition

**to**popular use

**.**

Suppose S is an immersed submanifold of M

**.**If the inclusion map i: S → M is closed then S is actually an embedded submanifold of M**.**__Conversely__**,****if**S is an embedded submanifold which is also**a**closed__subset__then the inclusion map is closed**.**

Conversely and R

__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__

**,**given central idempotents

**a**< sub > 1 </ sub >,...,

**a**< sub > n </ sub >

**in**

__R__

**that**are pairwise orthogonal

**and**have sum 1

**,**then

__R__is the direct sum of the rings Ra < sub > 1 </ sub >,…, Ra < sub > n </ sub >.

**

__Conversely__**,****if**ƒ: I →__R__is absolutely continuous**and**thus differentiable almost everywhere**,****and**satisfies | ƒ ′(**x**)| ≤ K**for**almost all**x****in**I**,**then ƒ is Lipschitz continuous with Lipschitz constant at most K**.**__Conversely__

**,**it is possible

**to**2-colour

**a**K < sub > 5 </ sub > without creating

**any**monochromatic K < sub > 3 </ sub >, showing

**that**

__R__

**(**3

**,**3

**)**> 5

**.**

__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

**.**

__Conversely__

**,**an exhaustive firing test of the M1918 Chauchat

**in**

**.**30-06 was also carried out

**in**1994 near Chambersburg

**,**Pennsylvania

**,**by

__R__

**.**Keller

**and**W

**.**Garofalo

**.**

__Conversely__

**,**the following characterization of derived functors holds: given

**a**family of functors

__R__< sup > i </ sup >: A → B

**,**satisfying the above

**,**i

**.**e

**.**mapping short exact sequences

**to**long exact sequences

**,**

**such**

**that**

**for**every injective object I of A

**,**

__R__< sup > i </ sup >( I )= 0

**for**every positive i

**,**then these functors are the right derived functors of

__R__< sup > 0 </ sup >.

__Conversely__

**,**given

**a**Boolean ring

__R__

**,**we define the join operation by

**a**' b =

**a**+ b + ab

**,**

**and**the meet operation as multiplication

**.**

__Conversely__

**,**

**if**this identity holds

**in**

**a**ring

__R__

**for**all pairs of elements

**a**

**and**b of the ring

**,**then

__R__is commutative

**.**

Conversely and defines

__Conversely__

**,**Psychology

__defines__bottom-up processing as an approach wherein

**there**is

**a**progression from the individual elements

**to**the whole

**.**

__Conversely__

**,**

**a**system of n quantities v < sup > i </ sup >

**that**transform like the coordinates

**x**< sup > i </ sup > on V

__defines__

**a**contravariant vector

**.**

Thus

**,**b < sub > q </ sub > is**a**symmetric bilinear form over K with matrix A**.**__Conversely__**,****any**symmetric bilinear form b__defines__**a**quadratic form__Conversely__the building can be recovered from the BN pair

**,**so

**that**every BN pair canonically

__defines__

**a**building

**.**

__Conversely__

**,**

**any**operator satisfying the above properties

__defines__

**a**connection on E

**and**

**a**connection

**in**this sense is also known as

**a**covariant derivative on E

**.**

__Conversely__

**,**an Ehresmann connection H ⊂ TP

**(**or v: TP → V

**)**on P

__defines__

**a**principal G-connection ω

**if**

**and**

**only**

**if**it is G-equivariant

**in**the sense

**that**

**.**

__Conversely__

**,**

**any**

**such**one form

__defines__

**(**via pullback

**)**

**a**G-equivariant horizontal 1-form on P

**,**

**and**the space of principal G-connections is an affine space

**for**this space of 1-forms

**.**

__Conversely__

**,**singly even dimensional manifolds have

**a**skew-symmetric nondegenerate bilinear form on their middle dimension ;

**if**one

__defines__

**a**quadratic refinement of this

**to**

**a**quadratic form

**(**as on

**a**framed manifold ), one obtains the Arf invariant as

**a**mod 2 invariant

**.**

Conversely and binary

Conversely and function

__Conversely__

**,**sociology of law may help comparative law answer questions

**,**

**such**as: How do regulations

**in**different legal systems really

__function__

**in**the respective societies?

__Conversely__

**,**

**in**functional code

**,**the output value of

**a**

__function__depends

**only**on the arguments

**that**are input

**to**the

__function__

**,**so calling

**a**

__function__f twice with the same value

**for**an argument

**x**will produce the same result f

**(**

**x**

**)**both times

**.**

__Conversely__

**,**given

**a**harmonic

__function__

**,**it is the real part of an analytic

__function__

**,**

**(**at least locally ).

__Conversely__most

**(**but not all

**)**of the ASCII " control characters " have some control

__function__

**in**isolation

**,**therefore are not escape characters

**.**

__Conversely__

**,**given

**any**harmonic

__function__

**in**two dimensions

**,**it is the real part of an analytic

__function__

**,**at least locally

**.**

__Conversely__

**,**those who wish

**to**

__function__primarily as clinical ED physicians choose the CCFP route of certification

**.**

__Conversely__

**,**warming of an affected extremity may indicate

**a**disruption of the body's normal thermoregulatory vasoconstrictor

__function__

**,**which may sometimes indicate underlying CRPS

**.**

__Conversely__

**,**except

**in**dimension 2

**,**

**if**the curvature of

**a**Riemannian manifold has this form

**for**some

__function__K

**,**then the Bianchi identities imply

**that**K is constant

**and**thus

**that**the manifold is

**(**locally

**)**

**a**space form

**.**

__Conversely__

**,**

**any**equation can take the canonical form f

**(**

**x**

**)**= 0

**,**so equation solving is the same thing as computing

**(**or finding

**)**

**a**root of

**a**

__function__

**.**

Equipped with this notion of length

**,****a**Riemannian manifold is**a**metric space**,**meaning**that**it has**a**distance__function__d**(**p**,**q**)**whose value at**a**pair of points p**and**q is the distance from p**to**q**.**__Conversely__**,**the metric tensor itself is the derivative of the distance__function__**(**taken**in****a**suitable manner ).__Conversely__

**,**by the inverse

__function__theorem

**,**

**there**can be at most one value

**for**σ

**that**

**,**when applied as an input

**to**

**,**will result

**in**

**a**particular value

**for**C

**.**

__Conversely__

**,**culture decline is

**a**

__function__of the feckless mixture of Aryan

**,**with lesser ' animalistic ,' blood ...

__Conversely__

**,**

**if**it is too wet

**,**mud cakes

**in**the machinery

**and**moisture weighs down the material

**,**making it impossible

**for**the equipment

**to**

__function__without picking up large quantities of mud

**.**

__Conversely__

**,**

**a**single email address may be an alias

**and**have

**a**distribution

__function__

**to**many mailboxes

**.**

__Conversely__

**,**

**there**may be levels of production where marginal cost is higher than average cost

**,**

**and**average cost is an increasing

__function__of output

**.**

__Conversely__

**,**

**a**

__function__u: E < sub > 1 </ sub > → E < sub > 2 </ sub > defined on

**a**basis of E < sub > 1 </ sub > can be uniquely extended

**to**

**a**linear

__function__

**.**

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