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Every lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping.

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## Some Related Sentences

Every and lattice

__Every__Boolean algebra

**is**

**a**Heyting algebra when

**a**→ b

**is**defined as usual as ¬

**a**∨ b

**,**as

**is**every complete distributive

__lattice__when

**a**→ b

**is**taken to be

**the**supremum

**of**

**the**set

**of**all c for which

**a**∧ c ≤ b

**.**The open sets

**of**

**a**topological space form

**a**complete distributive

__lattice__and hence

**a**Heyting algebra

**.**

*

__Every__totally ordered set that**is****a**bounded__lattice__**is**also**a**Heyting algebra**,**where**is**equal to when**,**and 1 otherwise**.**__Every__complete

__lattice__

**is**also

**a**bounded

__lattice__

**,**which

**is**to say that

**it**has

**a**greatest and least

**element**

**.**

__Every__

__lattice__

**in**can be generated from

**a**basis for

**the**vector space by forming all linear combinations with integer coefficients

**.**

*

__Every__substructure**is****the**union**of****its**finitely generated substructures ; hence Sub ( A )**is**an algebraic__lattice__**.**
Also

**,****a**kind**of**converse holds:__Every__algebraic__lattice__**is**isomorphic to Sub ( A ) for some algebra A**.**__Every__complemented distributive

__lattice__has

**a**unique orthocomplementation and

**is**

**in**fact

**a**Boolean algebra

**.**

__Every__quasinormal subgroup

**is**

**a**modular subgroup

**,**that

**is**

**,**

**a**modular

**element**

**in**

**the**

__lattice__

**of**subgroups

**.**

Every and element

__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

**.**

** 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__Boolean algebra ( A

**,**∧, ∨) gives rise to

**a**ring ( A

**,**+, ·) by defining

**a**+ b := (

**a**∧ ¬ b ) ∨ ( b ∧ ¬

**a**) = (

**a**∨ b ) ∧ ¬(

**a**∧ b ) ( this operation

**is**called symmetric difference

**in**

**the**case

**of**sets and XOR

**in**

**the**case

**of**logic ) and

**a**· b :=

**a**∧ b

**.**The zero

__element__

**of**this ring coincides with

**the**0

**of**

**the**Boolean algebra ;

**the**multiplicative identity

__element__

**of**

**the**ring

**is**

**the**1

**of**

**the**Boolean algebra

**.**

__Every__repetition

**of**insertion sort removes an

__element__from

**the**input data

**,**inserting

**it**into

**the**correct position

**in**

**the**already-sorted list

**,**until no input elements remain

**.**

__Every__singleton

**is**

**a**terminal object

**,**with

**the**functions mapping all elements

**of**

**the**source sets to

**the**

**single**target

__element__as morphisms

**.**

__Every__

__element__s

**,**except

**a**possible greatest

__element__

**,**has

**a**unique successor ( next

__element__), namely

**the**least

__element__

**of**

**the**subset

**of**all elements greater than s

**.**

__Every__subset which has an upper bound has

**a**least upper bound

**.**

*

__Every__non-empty set**of**left ideals**of**R**,**partially ordered by inclusion**,**has**a**maximal__element__with respect to set inclusion**.**__Every__time

**a**pixel on

**a**triangle

**is**rendered

**,**

**the**corresponding texel (

**or**texture

__element__)

**in**

**the**texture must be found

**.**

__Every__non-inner automorphism yields

**a**non-trivial

__element__

**of**Out ( G ), but different non-inner automorphisms may yield

**the**same

__element__

**of**Out ( G ).

Every and structure

__Every__congruence relation has

**a**corresponding quotient

__structure__

**,**whose elements are

**the**equivalence classes (

**or**congruence classes ) for

**the**relation

**.**

__Every__group has

**a**presentation

**,**and

**in**fact many different presentations ;

**a**presentation

**is**often

**the**most compact way

**of**describing

**the**

__structure__

**of**

**the**group

**.**

__Every__algebraic

__structure__has

**its**own notion

**of**homomorphism

**,**namely any function compatible with

**the**operation ( s ) defining

**the**

__structure__

**.**

__Every__chapter contains

**a**comprehensive compilation all

**of**

**the**published examples

**of**

**the**reaction organized

**in**tables according to

**the**

__structure__

**of**

**the**starting material

**.**

__Every__Riemann surface

**is**

**a**two-dimensional real analytic manifold ( i

**.**e.,

**a**surface ), but

**it**contains more

__structure__( specifically

**a**complex

__structure__) which

**is**needed for

**the**unambiguous definition

**of**holomorphic functions

**.**

:

__Every__oriented prime closed 3-manifold can be cut along tori**,**so that**the**interior**of**each**of****the**resulting manifolds has**a**geometric__structure__with finite volume**.**
* " What

__Every__Programmer Should Know About Memory " by Ulrich Drepper — explains**the**__structure__**of**modern memory subsystems and suggests how to utilize them efficiently__Every__H *

**is**very special

**in**

__structure__:

**it**

**is**pure-injective ( also called algebraically compact ), which says more

**or**less that solving equations

**in**H *

**is**relatively straightforward

**.**

__Every__

__structure__

**is**associated with

**a**certain quantity

**of**energy

**,**which determines

**the**stability

**of**

**the**molecule

**or**ion (

**the**lower energy

**,**

**the**greater stability ).

__Every__Hermitian manifold

**is**

**a**complex manifold which comes naturally equipped with

**a**Hermitian form and an integrable

**,**almost complex

__structure__

**.**

__Every__animal cell

**is**enclosed

**in**

**a**plasma membrane

**,**which has

**the**

__structure__

**of**

**a**lipid bilayer with many types

**of**large molecules embedded

**in**

**it**

**.**

__Every__

__structure__from

**the**World's Columbian Exposition was long ago destroyed by fire

**,**demolished

**or**moved elsewhere

**,**except for

**the**old Palace

**of**Fine Arts

**,**now

**the**Museum

**of**Science and Industry

**,**The Palace

**of**Fine Arts

**,**

**the**only fireproof building at

**the**fair

**,**fell into disrepair and was rehabilitated with

**a**$ 5 million grant

**in**1930 from Julius Rosenwald ( President

**of**Sears

**,**Roebuck and Co .).

__Every__five years

**,**starting

**the**day after Labor Day

**,**

**the**New Jersey Department

**of**Environmental Protection ’ s ( DEP ) water level management plan allows

**the**lake to be lowered five feet to allow for inspection

**of**

**the**dam

__structure__

**,**property owners ’ repairs to lakeshore structures

**,**aquatic vegetation control

**,**and silt and drainage material removal from areas around

**the**lake

**.**

__Every__timber

__structure__on

**the**site had been burnt

**,**

**the**charcoal being

**the**only organic matter that survived

**the**acid soils

**.**

__Every__( normal ) Boolean algebra with operators can be represented as

**a**field

**of**sets on

**a**relational

__structure__

**in**

**the**sense that

**it**

**is**isomorphic to

**the**complex algebra corresponding to

**the**field

**.**

__Every__compact smooth manifold

**of**dimension 2n

**,**which has only handles

**of**index ≤ n

**,**has

**a**Stein

__structure__provided n > 2

**,**and when n = 2

**the**same holds provided

**the**2-handles are attached with certain framings ( framing less than

**the**Thurston-Bennequin framing ).

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