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Formally, a profinite group is a Hausdorff, compact, and totally disconnected topological group: that is, a topological group that is also a Stone space.

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## Some Related Sentences

Formally and group

__Formally__

**,**this means symmetry under

**a**sub-group of the Euclidean

__group__of isometries in two or three dimensional Euclidean

**space**

**.**

__Formally__

**,**collective noun forms such as “

**a**

__group__of people ” are represented by second-order variables

**,**or by first-order variables standing for sets ( which are well-defined objects in mathematics

**and**logic ).

Informally

**,**G has the above presentation if it**is**the " freest__group__" generated by S subject only to the relations R**.**__Formally__**,**the__group__G**is**said to have the above presentation if it**is**isomorphic to the quotient of**a**free__group__on S by the normal subgroup generated by the relations R**.**__Formally__

**,**

**a**ring

**is**an Abelian

__group__( R

**,**+), together with

**a**second binary operation * such

**that**for all

**a**

**,**b

**and**c in R

**,**

* Blades ( hip-hop

__group__) (__Formally__Blades Of Hades ), Australian hip hop__group__from Newcastle**,**New South Wales__Formally__

**,**

**a**frieze

__group__

**is**

**a**class of infinite discrete symmetry groups for patterns on

**a**strip ( infinitely wide rectangle ), hence

**a**class of groups of isometries of the plane

**,**or of

**a**strip

**.**

__Formally__

**,**the

__group__was called Studiengesellschaft für Geistesurgeschichte ‚ Deutsches Ahnenerbe e

**.**V

**.**

__Formally__

**,**the Mahalanobis distance of

**a**multivariate vector from

**a**

__group__of values with mean

**and**covariance matrix

**is**defined as

**:**

__Formally__

**,**let G be

**a**Coxeter

__group__with reduced root system R

**and**k < sub > v </ sub >

**a**multiplicity function on R ( so k < sub > u </ sub > = k < sub > v </ sub > whenever the reflections σ < sub > u </ sub >

**and**σ < sub > v </ sub > corresponding to the roots u

**and**v are conjugate in G ).

__Formally__

**,**define the set of lines in the plane P as L ( P ); then

**a**rigid motion of the plane takes lines to lines – the

__group__of rigid motions acts on the set of lines –

**and**one may ask which lines are unchanged by an action

**.**

__Formally__Roman Kalyn

**is**now the only member of the

__group__

**,**but de-facto GreenJolly exists in name only

**.**

__Formally__

**,**

**a**redistribution of all agents ’ initial endowments of goods among all agents in the system

**is**

**a**core allocation if no

__group__of agents can redistribute their own initial endowments among themselves so as to improve the satisfaction of someone in the

__group__without impairing

**that**of any other in the

__group__

**.**

__Formally__

**,**this meant

**that**the whole peloton finished out of time limits

**,**but the referees understandably used

**a**rule saying

**that**they could give clemency to any

__group__of more than 20 % of the stage's starting riders

**,**officially citing the weather conditions as their reason to do so

**.**

__Formally__

**,**

**a**signed graph Σ

**is**

**a**pair ( G

**,**σ )

**that**consists of

**a**graph G = ( V

**,**E )

**and**

**a**sign mapping or signature σ from E to the sign

__group__

Formally and is

__Formally__organized vocational programs supported by federal funds allow high school students to gain experience in

**a**field of work which

__is__likely to lead to

**a**full-time job on graduation

**.**

__Formally__

**,**the set of all context-free languages

__is__identical to the set of languages accepted by pushdown automata ( PDA ).

More rigorously

**,**the divergence of**a**vector field F at**a**point p__is__defined as the limit of the net flow of F across the smooth boundary of**a**three dimensional region V divided by the volume of V as V shrinks to p**.**__Formally__**,**__Formally__

**,**the base

__is__known as Naval Support Facility Diego Garcia ( the US activity ) or Permanent Joint Operating Base ( PJOB ) Diego Garcia ( the UK's term ).

__Formally__

**,**there

__is__

**a**clear distinction

**:**" DFT " refers to

**a**mathematical transformation or function

**,**regardless of how it

__is__computed

**,**whereas " FFT " refers to

**a**specific family of algorithms for computing DFTs

**.**

__Formally__

**,**oxidation state

__is__the hypothetical charge

**that**an atom would have if all bonds to atoms of different elements were 100 % ionic

**.**

__Formally__

**,**an inner product

**space**

__is__

**a**vector

**space**V over the field together with an inner product

**,**i

**.**e., with

**a**map

__Formally__

**,**if M

__is__

**a**set

**,**the identity function f on M

__is__defined to be

**that**function with domain

**and**codomain M which satisfies

*

__Formally__**,**when working over the reals**,**as here**,**this__is__accomplished by considering the limit as ε → 0 ; but the " infinitesimal " language generalizes directly to Lie groups over general rings**.**__Formally__

**,**this sharing of dynamics

__is__referred to as universality

**,**

**and**systems with precisely the same critical exponents are said to belong to the same universality class

**.**

__Formally__

**,**

**a**frame

__is__defined to be

**a**lattice L in which finite meets distribute over arbitrary joins

**,**i

**.**e

**.**every ( even infinite ) subset

Formally and compact

__Formally__

**,**

**a**cardinal κ

**is**defined to be weakly

__compact__if it

**is**uncountable

**and**for every function f

**:**< sup > 2 </ sup > →

Formally and topological

__Formally__

**,**

**a**ringed

**space**( X

**,**O < sub > X </ sub >)

**is**

**a**

__topological__

**space**X together with

**a**sheaf of rings O < sub > X </ sub > on X

**.**

Formally and also

__Formally__the " head of state " can

__also__personally be the " head of government " ( ex officio or by ad hoc cumulation such as an absolute monarch nominating himself ) but otherwise has formal precedence over the Head of Government

**and**other ministers

**,**whether he

**is**their actual political superior ( absolute monarch

**,**executive president ) or rather theoretical or ceremonial in character

**.**

__Formally__

**,**Minkowski

**space**

**is**

**a**four-dimensional real vector

**space**equipped with

**a**nondegenerate

**,**symmetric bilinear form with signature < tt >(−,+,+,+)</ tt > ( Some may

__also__prefer the alternative signature < tt >(+,−,−,−)</ tt >; in general

**,**mathematicians

**and**general relativists prefer the former while particle physicists tend to use the latter

**.**

__Formally__

**,**this means

**that**

**,**for some function f

**,**the image f ( D ) of

**a**directed set D ( i

**.**e

**.**the set of the images of each element of D )

**is**again directed

**and**has as

**a**least upper bound the image of the least upper bound of D

**.**One could

__also__say

**that**f preserves directed suprema

**.**

__Formally__

**,**an ultrametric

**space**

**is**

**a**set of points with an associated distance function (

__also__called

**a**metric )

__Formally__

**,**however

**,**the role

__also__carries the title of " Klingon supreme commander " ( TNG's " Reunion "), which presumably means commander-in-chief of the military

**.**

Dick Smith Electronics has

__also__long been known for its " home brand " range of electronics which fall under the brand name " Dick Smith " (__Formally__called DSE**,****a**commonly used abbreviation of Dick Smith Electronics ).__Formally__

**,**he

**is**

__also__chief of staff of the air force

**and**navy as well

**,**but apparently the commanders of the other two services frequently report directly to the Minister of Defence / Commander-in-Chief

**.**

__Formally__the Airframe Reconditioning Squadron RNZAF

**,**the unit was commercialised in 1998

**and**

**is**now managed by SAFE Air Ltd

**.**No

**.**1 Repair Depot was

__also__active at the base for

**a**number of years

**,**though during the war it appears to have been stationed at Hamilton

**.**

__Formally__( see quote from Lewis

**,**below ), it can

__also__occur between nonallelic regions of the genome as well as regions of the genome

**that**are not transcribed

**.**

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