[permalink] [id link]

* Every preorder can be given a topology, the Alexandrov topology ; and indeed, every preorder on a set is in one-to-one correspondence with an Alexandrov topology on that set.

from
Wikipedia

## Some Related Sentences

Every and preorder

*****

__Every__finite topological space gives rise to

**a**

__preorder__

**on**its points

**,**

**in**which x ≤ y if

**and**only if x belongs to

**every**neighborhood of y

**,**

**and**

**every**finite

__preorder__

**can**

**be**formed as

**the**specialization

__preorder__of

**a**topological space

**in**this way

**.**

__Every__binary relation R

**on**

**a**

**set**S

**can**

**be**extended to

**a**

__preorder__

**on**S by taking

**the**transitive closure

**and**reflexive closure

**,**R < sup >+=</ sup >.

__Every__interior algebra

**can**

**be**represented as

**a**

__preorder__field

**with**its interior

**and**closure operators corresponding to those of

**the**

**Alexandrov**

**topology**induced by

**the**

__preorder__

**.**

Every and can

__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**

**.**

__Every__information exchange between living organisms — i

**.**e

**.**transmission of signals

**that**involve

**a**living sender

**and**receiver

__can__

**be**considered

**a**form of communication

**;**

**and**even primitive creatures such as corals are competent to communicate

**.**

__Every__context-sensitive grammar which does not generate

**the**empty string

__can__

**be**transformed into

**an**equivalent one

**in**Kuroda normal form

**.**

__Every__grammar

**in**Chomsky normal form

**is**context-free

**,**

**and**conversely

**,**

**every**context-free grammar

__can__

**be**transformed into

**an**equivalent one which

**is**

**in**Chomsky normal form

**.**

__Every__module over

**a**division ring has

**a**basis

**;**linear maps between finite-dimensional modules over

**a**division ring

__can__

**be**described by matrices

**,**

**and**

**the**Gaussian elimination algorithm remains applicable

**.**

__Every__entire function

__can__

**be**represented as

**a**power series

**that**converges uniformly

**on**compact sets

**.**

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**.**__Every__sequence

__can__

**,**thus

**,**

**be**read

**in**three reading frames

**,**each of which will produce

**a**different amino acid sequence (

**in**

**the**

**given**example

**,**Gly-Lys-Pro

**,**Gly-Asn

**,**or Glu-Thr

**,**respectively ).

__Every__hyperbola

**is**congruent to

**the**origin-centered East-West opening hyperbola sharing its same eccentricity ε ( its shape

**,**or degree of " spread "),

**and**

**is**also congruent to

**the**origin-centered North-South opening hyperbola

**with**identical eccentricity ε —

**that**

**is**

**,**it

__can__

**be**rotated so

**that**it opens

**in**

**the**desired direction

**and**

__can__

**be**translated ( rigidly moved

**in**

**the**plane ) so

**that**it

**is**centered at

**the**origin

**.**

__Every__holomorphic function

__can__

**be**separated into its real

**and**imaginary parts

**,**

**and**each of these

**is**

**a**solution of Laplace's equation

**on**R < sup > 2 </ sup >.

__Every__species

__can__

**be**

**given**

**a**unique (

**and**

**,**one hopes

**,**stable ) name

**,**as compared

**with**common names

**that**are often neither unique nor consistent from place to place

**and**language to language

**.**

__Every__vector v

**in**determines

**a**linear map from R to taking 1 to v

**,**which

__can__

**be**thought of as

**a**Lie algebra homomorphism

**.**

__Every__use of modus tollens

__can__

**be**converted to

**a**use of modus ponens

**and**one use of transposition to

**the**premise which

**is**

**a**material implication

**.**

__Every__adult

**,**healthy

**,**sane Muslim who has

**the**financial

**and**physical capacity to travel to Mecca

**and**

__can__make arrangements for

**the**care of his / her dependants during

**the**trip

**,**must perform

**the**Hajj once

**in**

**a**lifetime

**.**

Every and be

__Every__man who dabbles

**in**

**the**market to make

**a**little easy money

**on**

**the**side

**and**suffers losses could at

**the**time hardly face his wife who was wondering how her husband could

__be__so dumb

**.**

__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__Wednesday night through Oct. 11 there will

__be__

**an**elaborate colored fountain display

**,**

**with**229 nozzles throwing jets of water up to 130 feet

**.**

__Every__time

**a**speech sound

**is**produced for

**a**

**given**phoneme

**,**it will

__be__slightly different from other utterances

**,**even for

**the**same speaker

**.**

*****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__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__person should

__be__identified uniquely as resident

**in**one place but where they happen to

__be__

**on**census day

**,**their de facto residence

**,**may not

__be__

**the**best place to count them

**.**

__Every__adult

**and**wise woman without husband although reserves

**the**right to accept concubinage for her employer / master without any coercion or force

**,**but Islamic scholars have consensus

**that**for sex relations options of Nikkah

**and**Muta should

__be__adopted instead of concubinage

**in**this era

**.**

George

__Every__claims**that****the**existence of " myths**in****the**Bible would now__be__admitted by nearly everyone ", including " probably all Roman Catholics**and****a**majority of Protestants ".
According to

__Every__**,**one example may__be__"**the**myth of St**.**George "**and**other stories about saints battling dragons**,**which were " modelled no doubt**in**many cases**on**older representations of**the**creator**and**preserver of**the**world**in**combat**with**chaos ".0.078 seconds.