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* Every non-empty set of left ideals of R, partially ordered by inclusion, has a maximal element with respect to set inclusion.

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## Some Related Sentences

Every and non-empty

** Zorn's lemma:

__Every____non-empty__**partially****ordered****set**in which every chain ( i**.**e**.**totally**ordered**subset )**has**an upper bound contains at least one**maximal****element****.**
** Tukey's lemma:

__Every____non-empty__collection**of**finite character**has****a****maximal****element****with****respect****to****inclusion****.**__Every__

__non-empty__intersection

**of**

**a**3-sphere

**with**

**a**three-dimensional hyperplane is

**a**2-sphere ( unless the hyperplane is tangent

**to**the 3-sphere

**,**in which case the intersection is

**a**single point ).

*****

__Every__

__non-empty__Baire space is

**of**second category in itself

**,**and every intersection

**of**countably many dense open subsets

**of**X is

__non-empty__

**,**but the converse

**of**neither

**of**these is true

**,**as is shown

**by**the topological disjoint sum

**of**the rationals and the unit interval 1

**.**

__Every__

__non-empty__file must have at least one fork

**,**and depending on the file system

**,**

**a**file may have one or more other associated forks

**,**which in turn may contain primary data integral

**to**the file

**,**or just metadata

**.**

Every and set

__Every__such subset

**has**

**a**smallest

**element**

**,**so

**to**specify our choice function we can simply say that it maps each

__set__

**to**the least

**element**

**of**that

__set__

**.**

The restricted principle "

__Every__**partially****ordered**__set__**has****a****maximal**totally**ordered**subset " is also equivalent**to**AC over ZF**.*******

__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__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

**.**

__Every__subset A

**of**the vector space is contained within

**a**smallest convex

__set__( called the convex hull

**of**A ), namely the intersection

**of**all convex sets containing A

**.**

__Every__corporation

**,**whether financial or union

**,**as well as every division

**of**the administration

**,**were

__set__up as branches

**of**the party

**,**the CEOs

**,**Union leaders

**,**and division directors being sworn-in as section presidents

**of**the party

**.**

__Every__DNS zone must be assigned

**a**

__set__

**of**authoritative name servers that are installed in NS records in the parent zone

**,**and should be installed (

**to**be authoritative records ) as self-referential NS records on the authoritative name servers

**.**

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**.**
# " Personality " Argument: this argument is based on

**a**quote from Hegel: "__Every__man**has**the right**to**turn his will upon**a**thing or make the thing an object**of**his will**,**that is**to**say**,****to**__set__aside the mere thing and recreate it as his own ".__Every__atom across this plane

**has**an individual

__set__

**of**emission cones .</ p > < p > Drawing the billions

**of**overlapping cones is impossible

**,**so this is

**a**simplified diagram showing the extents

**of**all the emission cones combined

**.**

*****

__Every__preorder can be given

**a**topology

**,**the Alexandrov topology ; and indeed

**,**every preorder on

**a**

__set__is in one-to-one correspondence

**with**an Alexandrov topology on that

__set__

**.**

__Every__binary relation

**R**on

**a**

__set__S can be extended

**to**

**a**preorder on S

**by**taking the transitive closure and reflexive closure

**,**

**R**< sup >+=</ sup >.

Every and left

__Every__January 19

**,**in the early hours

**of**the morning

**,**the person made

**a**toast

**of**cognac

**to**Poe's original grave marker and

__left__three roses

**.**

If the book itself

**,**Animal Farm**,**had__left__any doubt**of**the matter**,**Orwell dispelled it in his essay Why I Write: '__Every__line**of**serious work that I ’ ve written since 1936**has**been written directly or indirectly against Totalitarianism ... dot**,**dot**,**dot**,**dot**.**__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__

__left__ideal I in

**R**is finitely generated

**,**i

**.**e

**.**there exist elements

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

**a**< sub > n </ sub > in I such that I = Ra < sub > 1 </ sub > + ... + Ra < sub > n </ sub >.

__Every__one

**of**the features encompassed

**by**the theory still requires

**a**reason for it

**to**be maintained after hominids

__left__the aquatic environment

**.**

__Every__year since 1880

**,**the organizations

**of**the French

__left__have held

**a**demonstration in this symbolic place during the last week

**of**May

**.**

"

__Every__part**of**his body**has**been replaced**,****with**the exception**of**" all the diodes down__left__side ," which have been giving him severe pain for the whole**of**his existence**.**__Every__actor provided multiple voices

**,**although the distinctive baritone

**of**Earle Hyman ( Panthro )

__left__the actor providing only very occasional guest voices in comparison

**with**his fellow performers

**.**

__Every__factual error

__left__in the published records is officially considered

**to**be

**a**failure

**by**the responsible officer

**.**

__Every__week

**,**he

__left__her food near the statue

**,**which was placed outside the house

**,**but nobody knew he was doing it

**.**

__Every__seat in the ballpark is green

**,**except for two-one in

__left__field which marks the spot

**of**Cal Ripken's 278th career homerun

**,**breaking Ernie Banks'all time record among shortstops

**,**and one in right field

**,**which marks the spot

**of**Eddie Murray's 500th career homerun

**.**

__Every__chain either

**has**the middle tile on the outside ( O ) or the inside ( I )

**of**the chain ; if it is arranged so that the indicator tile is

**to**the right

**of**the middle tile

**,**then the position

**of**the ring segment on the indicator tile can either be the upper

__left__( UL ), upper right ( UR ), lower

__left__( LL ) or lower right ( LR ) corner

**.**

__Every__day

**,**she saw trucks loaded

**with**Jews heading

**to**the railway station from where the trains

__left__for concentration camps

**.**

__Every__member

**of**the Queen's Royal Hussars

**of**the United Kingdom light cavalry wears the Maid

**of**Warsaw

**,**the crest

**of**the City

**of**Warsaw

**,**on the

__left__sleeve

**of**his No

**.**2 ( Service ) Dress

**.**

__Every__Samhain

**,**the phantom Aillén mac Midgna

**,**or Aillén the Burner

**,**would terrorize Tara

**,**playing music on his harp that

__left__every warrior helpless

**.**

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