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Every open subgroup H is also closed, since the complement of H is the open set given by the union of open sets gH for g in G

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## Some Related Sentences

Every and open

__Every__night they all went to Mama and Papa Albright's

**,**and sat on

**the**

__open__front porch

**,**where they could get

**the**breeze.

When coming to Kubla Khan

**,**he pointed out: " instead**of**being content to have written finely under**the**influence**of**laudanum**,**recommends ' Kubla-Khan ' to his readers**,**not as a poem**,**but as ' a psychological curiosity ' ...__Every__lover**of**books**,**scholar or not**,**who knows what it**is**to have his quarto__open__against a loaf at his tea ... ought to be**in**possession**of**Mr. Coleridge's poems**,**if it**is**only**for**' Christabel ', ' Kubla Khan ', and**the**' Ancient Mariner '.__Every__judgment contained

**the**reasons behind

**the**decision and

**the**judges assenting ; if there was a dissenting judge

**,**he was allowed to deliver his own judgment

**,**with all judgments read

**in**

__open__court before

**the**agents

**of**

**the**parties to

**the**dispute.

__Every__day

**,**doors seem to

__open__

**,**and every day

**,**we interact

**,**perhaps more than ever before

**,**with

**the**world outside.

__Every__map that

**is**injective

**,**continuous and either

__open__or

**closed**

**is**an embedding ; however there are

**also**embeddings which are neither

__open__nor

**closed**.

__Every__year

**,**Eton employs a ' Director-in-Residence ', an external professional director on a one-year contract who normally directs one house play and

**the**Lower Boy play ( a school play

__open__solely to

**the**first two year groups ), as well as teaching Drama and Theatre Studies to most year groups.

__Every__microwave oven sold has a protective interlock so that it cannot be run when

**the**door

**is**

__open__or improperly latched.

__Every__Tuesday and Saturday mornings

**in**

**the**summer near

**the**old train station a farmers ' market

**is**

__open__

**,**where farmers sell their fresh goods.

__Every__week

**of**

**the**Michaelmas and Lent terms

**,**and twice

**in**Easter term

**,**Churchill

**is**host to Pav

**,**a music event unusual

**for**Cambridge events

**in**that it

**is**free and

__open__to all university members.

__Every__mRNA consists

**of**three parts-5 ' untranslated region ( 5 ' UTR ), protein-coding region or

__open__reading frame ( ORF ) and 3 ' untranslated region ( 3 ' UTR ).

__Every__smooth manifold defined

**in**this way has a natural diffeology

**,**

**for**which

**the**plots correspond to

**the**smooth maps from

__open__subsets

**of**R < sup > n </ sup > to

**the**manifold.

__Every__summer

**,**operas

**,**music and drama are performed

**in**

**the**

__open__air at

**the**Freilichtbühne during

**the**month-long Wetzlar Festival (" Wetzlarer Festspiele ").

__Every__year there

**is**a famous cross-country ski race called

**the**Engadin Skimarathon from Maloja

**,**across

**the**frozen lakes and over

**the**

__open__meadows and ending

**in**S-chanf.

Every and subgroup

*

__Every__**closed**__subgroup__**of**a profinite group**is**itself profinite ;**the**topology arising from**the**profiniteness agrees with**the**subspace topology.
*

__Every__finitely generated group with a recursively enumerable presentation and insoluble word problem**is**a__subgroup__**of**a finitely presented group with insoluble word problem__Every__

__subgroup__

**of**a topological group

**is**itself a topological group when

**given**

**the**subspace topology.

__Every__

__subgroup__

**of**a free abelian group

**is**itself free abelian

**,**which

**is**important

**for**

**the**description

**of**a general abelian group as a cokernel

**of**a homomorphism between free abelian groups.

__Every__group

**of**prime order

**is**cyclic

**,**

**since**Lagrange's theorem implies that

**the**cyclic

__subgroup__generated

**by**

Iwasawa worked with so-called-extensions: infinite extensions

**of**a number field with Galois group isomorphic to**the**additive group**of**p-adic integers**for**some prime p.__Every__**closed**__subgroup__**of****is****of****the**form**,**so**by**Galois theory**,**a-extension**is****the**same thing as a tower**of**fields such that.
*

__Every__triangle group T**is**a discrete__subgroup__**of****the**isometry group**of****the**sphere ( when T**is**finite ),**the**Euclidean plane ( when T has a Z + Z__subgroup__**of**finite index ), or**the**hyperbolic plane.
Recall that a subsemigroup

**G****of**a semigroup S**is**a__subgroup__**of**S (**also**called sometimes a group**in**S ) if there exists an idempotent e such that**G****is**a group with identity element e. A semigroup S**is**group-bound if some power**of**each element**of**S lies**in**some__subgroup__**of**S.__Every__finite semigroup**is**group-bound**,**but a group-bound semigroup might be infinite.__Every__

__subgroup__

**is**organized around a

**set**

**of**brothers

**,**each

**of**whom

**is**often married to a group

**of**sisters.

__Every__finite group

**is**a

__subgroup__

**of**

**the**mapping class group

**of**a

**closed**

**,**orientable surface

**,**moreover one can realize any finite group as

**the**group

**of**isometries

**of**some compact Riemann surface.

__Every__proper

__subgroup__

**of**

**G**can be assumed a solvable group

**,**meaning that much theory

**of**such subgroups could be applied.

__Every__quasinormal

__subgroup__

**is**a modular

__subgroup__

**,**that

**is**

**,**a modular element

**in**

**the**lattice

**of**subgroups.

__Every__group has itself (

**the**improper

__subgroup__) and

**the**trivial

__subgroup__as two

**of**its fully characteristic subgroups.

Every and H

__Every__homomorphism f:

**G**→

__H__

**of**Lie groups induces a homomorphism between

**the**corresponding Lie algebras and.

The last two lines

**of****the**Act IV-scene 2 funeral song may**also**have inspired**the**lines W.__H__. Auden**,****the**librettist**for**Stravinsky's The Rake's Progress**,**puts into**the**mouth**of**Anne Truelove at**the**end**of****the**opera: "__Every__wearied body must late or soon return to dust ".__Every__adult citizen

**of**this small settlement signed

**the**small petition ; E. K Dyer and his wife

**,**William Johnson

**,**Joseph Otis and his wife

**,**Hiram Walker and his wife

**,**Joseph Pease and R.

__H__. Valentine.

__Every__quantum mechanical observable corresponds to a unique function or distribution on phase space

**,**and vice versa

**,**as specified

**by**Hermann Weyl ( 1927 ) and supplemented

**by**John von Neumann ( 1931 ); Eugene Wigner ( 1932 ); and

**,**

**in**a grand synthesis

**,**

**by**

__H__J Groenewold ( 1946 ).

__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__chain may run

**in**

**the**same direction to form a parallel sheet

**,**every other chain may run

**in**

**the**reverse chemical direction to form an anti parallel sheet

**,**or

**the**chains may be parallel and anti parallel to form a mixed sheet. The pattern

**of**

__H__bonding

**is**different

**in**

**the**parallel and anti parallel configurations.

*

__Every__finite-dimensional simple algebra over R must be a matrix ring over R**,**C**,**or__H__.__Every__central simple algebra over R must be a matrix ring over R or__H__. These results follow from**the**Frobenius theorem.__Every__graph has a harmonious coloring

**,**

**since**it suffices to assign every vertex a distinct color ; thus χ < sub >

__H__</ sub >(

**G**) ≤ | V (

**G**)|.

__Every__morphism f:

**G**→

__H__

**in**Grp has a category-theoretic kernel (

**given**

**by**

**the**ordinary kernel

**of**algebra ker f =

__Every__polytype can have monoclinic ( M ) or hexagonal (

__H__) symmetry

**,**and therefore some sources label them

**,**

**for**example

**,**not as 6C

**,**but 6H or 6M depending on

**the**symmetry.

Its publications include

__Every__Stony Acre Has a Name: Celebration**of****the**Townland**in**Ulster**by**Tony Canavan**,**and Townlands**in**Ulster: Local History Studies**,**edited**by**W.__H__.
She

**also**provided a technical review**of****the**educational text book " The Physics**of**__Every__Day Phenomena "**by**Thomas Griffith ( McGraw-Hill ), “ Physics**for****the**Life Sciences "**by**Philip Kesten and David Tauk ( W.__H__.__Every__sitting U. S. President

**since**1960 ( Eisenhower

**,**John F. Kennedy

**,**Lyndon B. Johnson

**,**Richard Nixon

**,**Gerald Ford

**,**Jimmy Carter

**,**Ronald Reagan

**,**George

__H__. W. Bush

**,**Bill Clinton and George W. Bush ) has addressed a convention or attended an event at Cobo Center.

__Every__recent president has supported

**the**power

**of**impoundment including Presidents Ronald Reagan

**,**George

__H__. W. Bush

**,**Bill Clinton

**,**George W. Bush

**,**and Barack Obama.

__Every__complete

**,**connected

**,**simply-connected manifold

**of**constant negative curvature − 1

**is**isometric to

**the**real hyperbolic space

__H__< sup > n </ sup >.

0.417 seconds.