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Every compact Hausdorff space is also locally compact, and many examples of compact spaces may be found in the article compact space.

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## Some Related Sentences

Every and compact

*

__Every__topological**space**X**is**a dense subspace**of**a__compact__**space**having at most one point more than X**,**by**the**Alexandroff one-point compactification**.**
*

__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__entire function can

**be**represented as a power series that converges uniformly on

__compact__sets

**.**

*

__Every__**locally**__compact__regular**space****is**completely regular**,****and**therefore every**locally**__compact__**Hausdorff****space****is**Tychonoff**.**
*

__Every____compact__**Hausdorff****space****of**weight at most ( see Aleph number )**is****the**continuous image**of**( this does not need**the**continuum hypothesis**,**but**is**less interesting**in**its absence ).__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__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 and Hausdorff

__Every__finite-dimensional

__Hausdorff__topological vector

**space**

**is**reflexive

**,**because J

**is**bijective by linear algebra

**,**

**and**because there

**is**a unique

__Hausdorff__vector

**space**topology on a finite dimensional vector

**space**

**.**

Every and space

__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__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__node on

**the**Freenet network contributes storage

__space__to hold files

**,**

**and**bandwidth that it uses to route requests from its peers

**.**

*

__Every__Lie group**is**parallelizable**,****and**hence an orientable manifold ( there**is**a bundle isomorphism between its tangent bundle**and****the**product**of**itself with**the**tangent__space__at**the**identity )__Every__vector

__space__has a basis

**,**

**and**all bases

**of**a vector

__space__have

**the**same number

**of**elements

**,**called

**the**dimension

**of**

**the**vector

__space__

**.**

__Every__normed vector

__space__V sits as a dense subspace inside a Banach

__space__; this Banach

__space__

**is**essentially uniquely defined by V

**and**

**is**called

**the**completion

**of**V

**.**

Every and is

__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__detail

**in**his interpretation has been beautifully thought out

**,**

**and**

**of**these I would especially cite

**the**delicious laendler touch

**the**pianist brings to

**the**fifth variation ( an obvious indication that he

__is__playing with Viennese musicians )

**,**

**and**

**the**gossamer shading throughout

**.**

__Every__taxpayer

__is__well aware

**of**

**the**vast size

**of**our annual defense budget

**and**most

**of**our readers

**also**realize that a large portion

**of**these expenditures go for military electronics

**.**

__Every__few days

**,**

**in**

**the**early morning

**,**as

**the**work progressed

**,**twenty men would appear to push it ahead

**and**to shift

**the**plank foundation that distributed its weight widely on

**the**Rotunda pavement

**,**supported as it

__is__by ancient brick vaulting

**.**

__Every__dream

**,**

**and**this

__is__true

**of**a mental image

**of**any type even though it

**may**

**be**readily interpreted into its equivalent

**of**wakeful thought

**,**

__is__a psychic phenomenon for which no explanation

__is__available

**.**

__Every__library borrower

**,**or at least those whose taste goes beyond

**the**five-cent fiction rentals

**,**knows what it

__is__to hear

**the**librarian say apologetically

**,**`` I'm sorry

**,**but we don't have that book

**.**

__Every__community

**,**if it

__is__alive has a spirit

**,**

**and**that spirit

__is__

**the**center

**of**its unity

**and**identity

**.**

The restricted principle "

__Every__partially ordered set has a maximal totally ordered subset "__is__**also**equivalent to AC over ZF**.**__Every__natural-born citizen

**of**a foreign state who

__is__

**also**an American citizen

**and**every natural-born American citizen who

__is__a citizen

**of**a foreign land owes a double allegiance

**,**one to

**the**United States

**,**

**and**one to his homeland (

**in**

**the**event

**of**an immigrant becoming a citizen

**of**

**the**US ), or to his adopted land (

**in**

**the**event

**of**an emigrant natural born citizen

**of**

**the**US becoming a citizen

**of**another nation ).

__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__year

**,**on

**the**last Sunday

**in**April

**,**there

__is__an ice fishing competition

**in**

**the**frozen estuarine waters

**of**

**the**Anadyr River's mouth

**.**

__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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