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Conversely, for any topology the clopen ( i. e. closed and open ) subsets yield a Boolean algebra.

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## Some Related Sentences

Conversely and for

__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__

**,**some elements do not maintain distinct allotropes in different phases –

__for__example phosphorus has numerous solid allotropes

**,**which all revert to

**the**same P < sub > 4 </ sub > form when melted to

**the**liquid state

**.**

__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__

**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__

**,**many fighter aircraft

**,**such as

**the**F-16

**,**are often used as ' bomb trucks ,' despite being designed

__for__aerial combat

**.**

__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__

**,**certain general principles

**(**

__for__example

**,**neighbourliness

**,**or charity

**)**are seen to be universal

**and**consistent

**.**

__Conversely__

**,**in more recent times

**,**Russian existentialist philosopher Lev Shestov viewed Job as

**the**embodiment of

**the**battle between reason

**(**which offers general

**and**seemingly comforting explanations

__for__complex events

**)**

**and**faith in

**a**personal god

**,**

**and**one man's desperate cry

__for__him

**.**

__Conversely__

**,**

**the**vast majority of early attempts at proper excavation techniques failed to accurately measure or record stratigraphy

**,**thereby failing to provide

**a**secure context

__for__artefact finds making interpretations extremely limited in scope

**.**

__Conversely__

**,**in

**the**English language as

**a**whole

**,**singular verb forms can often be used with nouns ending in "- s " that were once considered plural

**(**

__for__example: " Physics is my favorite academic subject ").

__Conversely__

**,**Derek Bickerton

**and**others argue that

**the**advent of abstract words provided

**a**mental basis

__for__analyzing higher-order relations

**,**

**and**that

**any**communication system that remotely resembles human language utterly relies on cognitive architecture that co-evolved alongside language

**.**

__Conversely__

**,**

**the**tiny meson mass mass differences responsible

__for__meson oscillations are often expressed in

**the**more convenient inverse picoseconds

**.**

__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__

**,**

**the**bodies of people who had certain medical conditions are useful

__for__research into those conditions

**.**

__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__

**,**one might expect that inertial motions

**,**once identified by observing

**the**actual motions of bodies

**and**making allowances

__for__

**the**external forces

**(**such as electromagnetism or friction ), can be used to define

**the**geometry of space

**,**as well as

**a**time coordinate

**.**

__Conversely__

**,**

__for__many deductive systems

**,**it is possible to prove

**the**completeness theorem as an effective consequence of

**the**compactness theorem

**.**

Conversely and any

__Conversely__

**the**equilibrium position is said to be " far to

**the**left " if hardly

__any__product is formed from

**the**reactants

**.**

* 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__

**,**there are other stars that never rise above

**the**horizon

**,**as seen from

__any__given point on

**the**Earth's surface

**(**except exactly on

**the**equator ).

__Conversely__

**,**

__any__surjection between sets determines

**a**partition on its domain

**,**

**the**set of preimages of singletons in

**the**codomain

**.**

__Conversely__

**,**

**a**person may feel like he belongs to one state without having

__any__legal relationship to it

**.**

__Conversely__

**,**

**the**interior of

**the**box has

**a**constant

**,**zero potential energy .< ref > Actually

**,**

__any__constant

**,**finite potential can be specified within

**the**box

**.**

__Conversely__

**,**extremely thin jewelry can cause

**the**same tearing in what is commonly referred to as

**the**" cheese cutter effect ", either during sudden torsion or over

**a**long period of wearing

**,**especially if

**the**thin jewelry bears

__any__weight

**.**

__Conversely__

**,**

__any__Hermitian positive semidefinite matrix M can be written as M = A < sup >*</ sup > A ; this is

**the**Cholesky decomposition

**.**

__Conversely__

**,**if

**a**double sharp were added to

__any__other note not containing

**a**sharp or flat as indicated by

**the**key signature then

**the**note will be raised two semitones or

**a**whole step with respect to

**the**chromatic scale

**.**

__Conversely__

**,**supplementation with L-phenylalanine

**,**L-tyrosine

**,**L-DOPA

**,**or

__any__of

**the**cofactors will increase their respective concentrations

**.**

__Conversely__

**,**

__any__choice of μ

**,**full rank matrix U

**,**

**and**positive diagonal entries Λ < sub >

**i**</ sub > yields

**a**non-singular multivariate normal distribution

**.**

__Conversely__

**,**

**the**influence of

**the**data at

__any__given point on

**the**initial line propagates with

**the**finite velocity c: there is no effect outside

**a**triangle through that point whose sides are characteristic curves

**.**

__Conversely__

**,**given

__any__harmonic function in two dimensions

**,**it is

**the**real part of an analytic function

**,**at least locally

**.**

__Conversely__

**,**if

**the**Turing Machine is expected polynomial-time

**(**

**for**

__any__given x ), then

**a**considerable fraction of

**the**runs must be polynomial-time bounded

**,**

**and**

**the**coin sequence used in such

**a**run will be

**a**witness

**.**

It is

**a**fact that**the**ring is**a**principal ideal ring ; that is**,****for**__any__ideal I in**,**there exists an integer n in I such that every element of I is**a**multiple of n**.**__Conversely__**,****the**set of all multiples of an arbitrary integer n is necessarily an ideal**,****and**is usually denoted by**(**n ).0.071 seconds.