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) 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.

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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 B

__Conversely__

**,**off-centering

**of**an undersized

__B__cation within its octahedron allows

**it**to attain

**a**stable bonding pattern

**.**

__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__

**,**an Earth-like planet at 0

**.**71 AUs from α Cen

__B__( with

**a**revolution period

**of**0

**.**63 years

**)**would get Sun-like illumination from its primary

**,**

**and**α Cen A would appear 4

**.**6 to 7

**.**3 magnitudes dimmer (− 22

**.**

**1**to − 19

**.**4 ), 70 to 840 times dimmer than α Cen

__B__but still 5700 to 470 times brighter than

**the**full Moon

**.**

__Conversely__

**,**

**the**first

__B__

**.**A Rock festival ( now promoted

**by**Pinap magazine successor Revista Pelo ), had many

**of**

**the**artists

**and**bands that would lead

**the**Acoustic rock movement: Gustavo Santaolalla forming Arco Iris

**,**León Gieco's rock-folk hybrid

**,**Sui Generis

**and**

**the**start

**of**Charly García's music career

**,**Raul Porchetto

**,**

**and**Pedro y Pablo

**,**among other bands

**.**

__Conversely__

**,**

**for**GdCo magnets

**,**

__B__< sub > r </ sub > increases as temperature increases within certain temperature ranges

**.**

*

__Conversely__**,****if**G has**a**BN pair**of**rank**1****,****then****the**action**of**G**on****the**cosets**of**__B__**is**doubly transitive**.**__Conversely__

**,**

**if**

__B__( t

**)**

**is**

**a**Brownian bridge

**and**Z

**is**

**a**standard normal random variable

**,**

**then**

**the**process

In this Division

**the**teams played-off in order to get**a**promotion into Division A**.**__Conversely__**,****the**two worst performing teams**of**Division A were relegated into Division__B__**.**__Conversely__

**,**Line

__B__to

**the**Gare du Nord

**and**Line A towards Auber are

**both**located

**on**

**the**south platform

**.**

Conversely and satisfies

Given

**a**field ordering ≤ as in Def**1****,****the**elements such that x ≥ 0 forms**a**positive cone**of**F**.**__Conversely__**,**given**a**positive cone P**of**F as in Def**2****,**one can associate**a**total ordering ≤< sub > P </ sub >**by**setting x ≤ y to mean y − x ∈ P**.**This total ordering ≤< sub > P </ sub >__satisfies__**the**properties**of**Def**1****.**
**

__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__

**,**once

**a**basis

**for**A has been chosen

**,**

**the**products

**of**basis elements can be set arbitrarily

**,**

**and**

**then**extended in

**a**

**unique**way to

**a**bilinear operator

**on**A

**,**i

**.**e., so

**the**resulting multiplication

__satisfies__

**the**algebra laws

**.**

__Conversely__

**,**

**if**

**a**highest weight module

**is**integrable

**,**

**then**its highest weight vector v

__satisfies__

**,**where are complex numbers such that

__Conversely__

**,**any sequence that

__satisfies__

**a**linear recurrence determines

**a**rational function when used as

**the**coefficients

**of**

**a**Taylor series

**.**

**which**are linearly independent at each point q in U

**.**

__Conversely__

**,**given such

**a**coframe

**,**

**there**

**is**

**a**

**unique**moving frame

**X**< sub >

**1**</ sub >,

**X**< sub >

**2**</ sub >, ...,

**X**< sub > n </ sub >

**which**

**is**dual to

**it**

**,**i

**.**e.,

__satisfies__

**the**duality relation α < sup > i </ sup >(

**X**< sub > j </ sub >) = δ < sup > i </ sup >< sub > j </ sub >, where δ < sup > i </ sup >< sub > j </ sub >

**is**

**the**Kronecker delta function

**on**U

**.**

Conversely and both

__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

**.**

__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__

**,**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__

**,**

__both__owners

**of**capital

**and**labor profit in real terms from an increase in

**the**capital endowment

**.**

__Conversely__

**,**

**of**

**the**253 known stable nuclides

**,**only five have

__both__an odd number

**of**protons

**and**odd number

**of**neutrons: hydrogen-2 ( deuterium ), lithium-6

**,**boron-10

**,**nitrogen-14

**,**

**and**tantalum-180m

**.**

__Conversely__

**,**

**the**two sunniest months

**of**

**the**year

**;**

__both__in winter-June

**and**July

**,**

__both__receive an abundant daily average

**of**9

**.**0 hours

**of**sunshine

**.**

__Conversely__

**,**

**the**remarkably accurate calculation

**of**

**the**earth's circumference

**by**Eratosthenes

**,**

**and**

**the**invention

**of**

**a**steam engine

**by**Heron

**,**

__both__ascribed in chapter 60 to

**the**priest Menes

**,**historically occurred in Alexandrian Egypt

**,**centuries after

**the**period

**of**

**the**novel

**.**

His cold demeanour

**is**representative**of**what**the**sixteenth century thought to be**a**side-effect**of**political genius__Conversely__**,**Antony ’ s focus**is****on**valour**and**chivalry**,****and**Antony views**the**political power**of**victory as**a**by-product**of**__both__**.**__Conversely__

**,**studying surface

**of**earth leads to an understanding

**of**

**the**atmosphere

**and**climate

**of**

**a**planet —

__both__its present state

**and**its past

**.**

__Conversely__

**,**two

**of**

**the**most famous rock musicians from Ontario

**,**Avril Lavigne

**and**Alanis Morissette

**,**are Franco-Ontarian

**by**

**the**second definition but not

**by**

**the**first

**,**since they were born to Franco-Ontarian parents but currently work

**and**live predominantly using

**the**English language (

__both__currently have residences in Los Angeles ).

__Conversely__

**,**

**the**Battles

**of**Plataea

**and**Mycale were

__both__fought from

**a**relative position

**of**Greek strength

**,**

**and**against lesser odds

**;**perhaps

**the**Greeks were even expecting to win

**and**had certainly seen

**the**opportunity to deal

**the**final blow

**.**

__Conversely__

**,**this could mean Anulo was " nepos "

**of**

__both__

**the**senior Harald

**and**

**the**other King mentioned in

**the**same phrase

**,**Hemming

**.**

"

__Conversely__**,**in**the**positive sense**,****it**would refer to " having**it**__both__ways " or " having**the**best**of**__both__worlds**.**__Conversely__

**,**David H

**.**Rosenthal sees

**the**development

**of**hard bop as

**a**response to

__both__

**a**perceived decline in bebop

**and**

**the**rise

**of**rhythm

**and**blues

**.**

#

__Conversely__**,**many older British Jews consider**it**more colloquial**and**" down-home " to say " Shobbes ", " cholla "**and**" motza ", though**the**vowel in these words**is**in fact**a**patach**,****which****is**rendered as in__both__Sephardi**and**Ashkenazi Hebrew**.**__Conversely__

**,**mastery

**of**Rabbinic literature

**and**Talmud could be found in

__both__camps

**,**as scholars were also attracted to Hasidic philosophy

**.**

__Conversely__

**,**some

**of**

**the**Alliance party members who joined

**the**Alliance via other parties decided to leave

**the**Alliance

**and**join

**the**Green Party

**,**notably Sue Bradford

**and**Keith Locke

**,**who

__both__joined

**the**Alliance via NewLabour

**.**

__Conversely__

**,**certain Jewish Christian sects

**,**including

**the**Cerinthians

**,**recognized Mosaic law as

__both__practicable

**and**necessary

**.**

__Conversely__

**,**as

**the**lid

**is**closed one piece slides back

**,**

**then**

__both__slide inward until

**the**keyboard can be covered

**by**

**the**lid

**.**

__Conversely__

**,**Official Nintendo Magazines Tom East wrote that while Treecko

**is**similar to Snivy due to

__both__being " green reptiles ", " they look nothing like each other ".

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