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* Every compact space is σ-compact, and every σ-compact space is Lindelöf ( i. e. every open cover has a countable subcover ).

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Wikipedia

## 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__

__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 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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