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Formally and group
Formally, a profinite group is a Hausdorff, compact, and totally disconnected topological group: that is, a topological group that is also a Stone space.
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,
Formally, its group of conformal transformations is infinite dimensional.
Formally, a Coxeter group can be defined as a group with the presentation
* 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 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 was
Formally the Prince-Electors elected a King of the Romans, who was elected in Germany but became Holy Roman Emperor only when crowned by the Pope.
Formally it was part of Arles, but in reality it was under the influence of the French king.
Formally named " United Press Associations " for incorporation and legal purposes, but publicly known and identified as United Press or UP, it was created by the 1907 uniting of three smaller news syndicates by the Midwest newspaper publisher E. W. Scripps.
Formally a census-designated place ( CDP ), Laguna West-Lakeside was annexed by Elk Grove in 2003.
In late 1900s the day that of the City was founded is Jakin School is a Private School is Formally Part of Jakin School Board was Grades One through Twelve there is no Football field on this school. In 1966 When Jakin School was Closed were Sent to Blakely-Union Elementary, Junior High, and High School ( which later Became Early County High, Middle, and Elementary School ). while Carver school was built for African-American students grades One through Twelve. although late 1960s when Carver school was closed along with Kestler School was based in Damascus were sent to Washington High & Elementary at Blakely. In addition to small farm agriculture, Jakin's early economic growth resulted from turpentine.
Formally, it was ceded to Russia in the Treaty of Nystad in 1721, together with Swedish Estonia and Swedish Ingria.
Formally declared on October 9, 1970, the Khmer Republic was a right-wing pro-United States military-led government headed by General Lon Nol and Prince Sisowath Sirik Matak that took power in the March 18, 1970 coup against Prince Norodom Sihanouk, then the country's head of state.
Formally it was part of Serbia, but it actually was a virtually separate autonomous region ruled by its German minority.
Formally known as Motion Picture Distribution LP, it was re branded and relaunched in 2007 due to the break-up of its preceding company, Alliance Atlantis, which was sold off piece by piece to Canwest Global, GS Capital Partners, along with several other smaller companies.
Formally, the Cisalpine Republic was an independent state allied with France, but the treaty of alliance established the effective subalternity of the new republic to France.
Formally known as Sportsdesk, it was re-vamped to closer resemble ESPN's own SportsCenter ( including the use of its theme music, logo, and opening ) in the Fall of 2001 as part of a corporate restructuring, closer aligning itself with new minority owner ESPN.
Formally known as the Kelowna Grizzlies, the club was purchased in
Formally speaking, the opportunity was extended to all classes to join China's project on its Leninist terms.
Formally known as the Inverurie Parish Church, a split in Church of Scotland over the appointment of ministers in 1843 ( The Disruption ) led to the creation of the West Parish Church ( known locally as " The West Kirk ") which was founded as a Free Church ( a church free from Edinburgh control ) thus causing the Inverurie Parish Church to change its name.
Formally a member of the country's collective head of state and, as president of parliament, holder of the third-highest office, he was left with little political influence.
Formally known as the " Long Tinh ", the flag was the official flag of the Nguyễn Court.

Formally and called
Formally, a binary operation on a set S is called associative if it satisfies the associative law:
Formally, a topological space X is called compact if each of its open covers has a finite subcover.
Formally speaking, a collation method typically defines a total order on a set of possible identifiers, called sort keys, which consequently produces a total preorder on the set of items of information ( items with the same identifier are not placed in any defined order ).
Formally, a set S is called finite if there exists a bijection
Formally, these reside in a complex separable Hilbert space-variously called the " state space " or the " associated Hilbert space " of the system-that is well defined up to a complex number of norm 1 ( the phase factor ).
Formally, if is an open subset of the complex plane, a point of, and is a holomorphic function, then is called a removable singularity for if there exists a holomorphic function which coincides with on.
Formally, we have for the approximation to the full solution A, a series in the small parameter ( here called ), like the following:
Formally, they are partial derivatives of the option price with respect to the independent variables ( technically, one Greek, gamma, is a partial derivative of another Greek, called delta ).
Formally called " Willow Township "
Formally, however, a face is any of the lower dimensional boundaries of the polytope, more specifically called an n-face.
Formally, a hypergraph is a pair where is a set of elements called nodes or vertices, and is a set of non-empty subsets of called hyperedges or edges.
Formally, a Lie superalgebra is a ( nonassociative ) Z < sub > 2 </ sub >- graded algebra, or superalgebra, over a commutative ring ( typically R or C ) whose product, called the Lie superbracket or supercommutator, satisfies the two conditions ( analogs of the usual Lie algebra axioms, with grading ):
Formally, a Hopf algebra is a ( associative and coassociative ) bialgebra H over a field K together with a K-linear map S: H → H ( called the antipode ) such that the following diagram commutes:
Formally, an ultrametric space is a set of points with an associated distance function ( also called a metric )
Formally the neutral is called the “ grounded conductor ”; as of the 2008 NEC, the terms “ neutral conductor ” and “ neutral point ” have been defined in the Code to record what had been common usage.
Formally, the game ( coalitional game ) consists of a finite set of players, called the grand coalition, and a characteristic function denotes the power set of .</ ref > from the set of all possible coalitions of players to a set of payments that satisfies.
Formally called the Final Declaration of the Stresa Conference, its aim was to reaffirm the Locarno Treaties and to declare that the independence of Austria " would continue to inspire their common policy ".
Formally, a non-empty partially ordered set ( D, ≤) is called a Scott domain if the following hold:
Formally called " the Wigwam ", this immense edifice was located on Girard Avenue between 19th and 20th Streets, across from Philadelphia's Girard College.
Formally, the Ministry of Aeronautics was founded on January 20, 1941 and so its military branch called " National Air Forces ", changed to " Brazilian Air Force " ( Força Aérea Brasileira-FAB ) on May, 22.
Formally called Mills and Boon Classics and Mills and Boon Favourites.
Formally called The Best Of and Collection.
Formally called Modern Romance Extra.

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