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* 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 ).

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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**

**is**also locally

__compact__

**,**and many examples

**of**

__compact__spaces may be found

**in**

**the**article

__compact__

**space**.

__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 weight

__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.

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__day

**,**records were taken including what he did

**at**what time

**,**

__weight__

**,**and anything else

**of**note.

__Every__ship

**,**submarine

**,**and dirigible must be designed to displace a

__weight__

**of**fluid equal to

**its**own

__weight__.

__Every__wire was able to be traced from origin to destination with software and

**the**

__weight__

**of**

**the**cable interconnecting cabinets was automatically calculated by an RCA 501 machine language program named " signal path " written by Robert Goerss

**,**computing facility director.

__Every__

__weight__

**is**a

**number**between λ and − λ which differs from them by an integer and has multiplicity one.

__Every__time a variable

**in**grade

**,**traction

**,**or wheel slip occurs

**,**

**the**computer will adjust

**the**pressure

**in**these cylinders to maintain sufficient adhesion

**,**by varying

**the**

__weight__on

**the**drive axles.

__Every__square inch

**of**a giant bone had to support 10 times

**the**

__weight__borne by a square inch

**of**human bone.

0.406 seconds.