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Every subset of the Hilbert cube inherits from the Hilbert cube the properties of being both metrizable ( and therefore T4 ) and second countable.

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## Some Related Sentences

Every and subset

__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**.**
The restricted principle "

__Every__partially ordered set has a maximal totally ordered__subset__" is also equivalent to AC over ZF**.**__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__separable metric space is isometric to a__subset__**of****the****(**non-separable**)**Banach space l < sup >∞</ sup >**of**all bounded real sequences with**the**supremum norm ; this is known as**the**Fréchet embedding**.**
*

__Every__separable metric space is isometric to a__subset__**of**C (),**the**separable Banach space**of**continuous functions → R, with**the**supremum norm**.**__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__

__subset__

**of**a nowhere dense set is nowhere dense,

**and**

**the**union

**of**finitely many nowhere dense sets is nowhere dense

**.**

It is more interesting that

**the**converse also holds:__Every__**second****countable****T4**space is homeomorphic to a__subset__**of****the****Hilbert****cube****.**
*

__Every__totally disconnected compact metric space is homeomorphic to a__subset__**of**a**countable**product**of**discrete spaces**.**
*

__Every__irreducible closed__subset__**of**P < sup > n </ sup >( k**)****of**codimension one is a hypersurface ; i**.**e.,**the**zero set**of**some homogeneous polynomial**.**

Every and Hilbert

__Every__

__Hilbert__space X is a Banach space because, by definition, a

__Hilbert__space is complete with respect to

**the**norm associated with its inner product, where a norm

**and**an inner product are said to be associated if for all x ∈ X

**.**

__Every__building has a canonical length metric inherited

**from**

**the**geometric realisation obtained by identifying

**the**vertices with an orthonormal basis

**of**a

__Hilbert__space

**.**

*

__Every__Polish space is homeomorphic to a G < sub > δ </ sub > subspace**of****the**__Hilbert__**cube**,**and**every G < sub > δ </ sub > subspace**of****the**__Hilbert__**cube**is Polish**.****(**5

**)**

__Every__continuous affine isometric action

**of**G on a real

__Hilbert__space has a fixed point

**(**property

**(**FH )).

__Every__commutative von Neumann algebra on a separable

__Hilbert__space is isomorphic to L < sup >∞</ sup >( X

**)**for some standard measure space

**(**X, μ

**)**

**and**conversely, for every standard measure space X, L < sup >∞</ sup >( X

**)**is a von Neumann algebra

**.**

__Every__correspondence prescription between phase space

**and**

__Hilbert__space, however, induces its own proper-product

**.**

*

__Every__smooth__Hilbert__manifold can be smoothly embedded onto an open**subset****of****the**model__Hilbert__space**.**

Every and cube

__Every__magic

__cube__may be assigned to one

**of**six magic

__cube__classes, based on

**the**

__cube__characteristics

**.**

Every and inherits

__Every__human mind

__inherits__a complement

**of**species-specific “ elementary ideas ”

**(**Elementargedanken ),

**and**hence

**the**minds

**of**all people, regardless

**of**their race or culture, operate in

**the**same way

**.**

Every and from

__Every__morning early, in

**the**summer, we searched

**the**trunks

**of**

**the**trees as high as we could reach for

**the**locust shells, carefully detached their hooked claws

__from__

**the**bark where they hung,

**and**stabled them, a weird faery herd, in an angle between

**the**high roots

**of**

**the**tulip tree, where no grass grew in

**the**dense shade

**.**

__Every__legislator

__from__Brasstown Bald to Folkston is going to have his every vote subjected to

**the**closest scrutiny as a test

**of**his political allegiances, not his convictions

**.**

__Every__pitch in

**the**game brought forth a howl

__from__

**the**enraptured audience

**and**every fly ball

**the**visitors dropped

**(**

**and**because their right fielder was still a little fuzzy

__from__drink, they dropped many

**)**called forth yelps

**of**derision

**.**

__Every__line

**of**written text is a mere reflection

**of**references

__from__any

**of**a multitude

**of**traditions, or, as Barthes puts it, "

**the**text is a tissue

**of**quotations drawn

__from__

**the**innumerable centres

**of**culture "; it is never original

**.**

__Every__book followed a different train

**of**thought,

__from__inspiration to solution, according to her autobiography

**.**

__Every__time a speech sound is produced for a given phoneme, it will be slightly different

__from__other utterances, even for

**the**same speaker

**.**

__Every__year

**both**clubs play

**the**" Klassieker " (" The Classic "), a derby match between

**the**teams

__from__

**the**two largest cities

**of**

**the**Netherlands

**.**

Four other hits

__from__**the**album made**the**Pop top 20: "__Every__Heartbeat "**(**No**.**2 ), " That's What Love Is For "**(**No**.**7 ), " Good For Me "**(**No**.**8 ),**and**" I Will Remember You "**(**No**.**20 ).
* Revised Code

**of**Washington 9**.**12**.**010: "__Every__person who brings on his or her own behalf, or instigates, incites, or encourages another to bring, any false suit at law or in equity in any court**of**this state, with intent thereby to distress or harass a defendant in**the**suit, or who serves or sends any paper or document purporting to be or resembling a judicial process, that is not in fact a judicial process, is guilty**of**a misdemeanor ;**and**in case**the**person offending is an attorney, he or she may, in addition thereto be disbarred__from__practicing law within this state**.**__Every__character is automatically continuous

__from__A to C, since

**the**kernel

**of**a character is a maximal ideal, which is closed

**.**

__Every__year,

**the**European Joint Conferences on Theory

**and**Practice

**of**Software

**(**ETAPS

**)**sponsors

**the**International Conference on Compiler Construction

**(**CC ), with papers

__from__

**both**

**the**academic

**and**industrial sectors

**.**

__Every__Halloween, Dabney House conducts

**the**infamous " Millikan pumpkin-drop experiment "

__from__

**the**top

**of**Millikan Library,

**the**highest point on campus

**.**

*

__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__argues that "

**the**disparagement

**of**myth in our own civilization " stems partly

__from__objections to perceived idolatry, objections which intensified in

**the**Reformation,

**both**among Protestants

**and**among Catholics reacting against

**the**classical mythology revived during

**the**Renaissance

**.**

__Every__gun that is made, every warship launched, every rocket fired signifies, in

**the**final sense, a theft

__from__those who hunger

**and**are not fed, those who are cold

**and**are not clothed

**.**

In Norse mythology, Draupnir

**(**Old Norse "**the**dripper ") is a gold ring possessed by**the**god Odin with**the**ability to multiply itself:__Every__ninth night eight new rings ' drip '__from__Draupnir, each one**of****the**same size**and**weight as**the**original**.**__Every__time a diode switches

__from__on to off or vice versa,

**the**configuration

**of**

**the**linear network changes

**.**

*

__Every__June, Ellensburg hosts Dachshunds on Parade, an event that draws Dachshund dog owners__from__all over**the**Northwest**.**
For example

**the**words**of**" I'm a Man You Don't Meet__Every__Day "**(**Roud 975**)**are known__from__a broadside in**the**Bodleian Library**.**
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**.**0.978 seconds.