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Therefore the topology on a topologically finitely-generated profinite group is uniquely determined by its algebraic structure.
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Therefore and topology
In fact, the collection of all left cosets ( or right cosets ) of C in G is equal to the collection of all components of G. Therefore, the quotient topology induced by the quotient map from G to G / C is totally disconnected.
Therefore, each node knows the exact network topology, i. e. it has a graph representation of the network.
Therefore, if one would give the product topology of R < sup > N </ sup > where the topology of R is the usual topology rather than the discrete one, then the above limit would converge to exp ( X ).
Therefore it serves as one of the basic counterexamples of topology .< ref >
Therefore, the lower limit topology on the real line is not metrizable.
Therefore topology optimisation is used to generate concepts and shape optimisation is used to fine-tune a chosen design topology.
Therefore and on
Therefore, under our longstanding allocation rules, on some of these channels no station other than the dominant ( class 1 ) -- A ) station is permitted to operate at night, so that the 1, -- A station can render service, interference free, wherever it can be received.
Therefore, the lumber is bought in planks and ripped to size for battens, etc., on a table saw.
Therefore the second principle of the plan must be that, while providing for all-out hostilities, its effectiveness is not dependent on general war.
Therefore, the third principle of the plan must be that it does not depend for effectiveness on engagement by the same types, unless at an assured favorable exchange rate.
Therefore, the plan's fifth principle must be that it capitalize on the capabilities of all elements in combination.
Therefore, the sixth principle of the plan must be that it concentrate on current measures which will reduce future force requirements.
Therefore, the on-the-scene commander must have detailed operating instructions based on measurement of conditions, in the area, at the time of encounter.
Therefore, the only conceivable alternatives are those represented, on the one hand, by the two at least apparently self-consistent but mutually exclusive positions of Buri and Barth and, on the other hand, by the third but really pseudo position ( analogous to a round square ) of Bultmann.
Therefore, if a lower court has ruled in an improper manner, or against legal precedent, that judgment will stand if not appealed – even if it might have been overturned on appeal.
Therefore, all primordial americium ( americium that was present on Earth during its formation ) should have decayed by now.
Therefore there were only lifts on every second floor so people had to communicate with one another on different floors.
Therefore, potential risks of side-effects and effectiveness depend on the type of antibacterial administered.
Therefore the stability of the particular allotropes depends on particular conditions.
Therefore, on 13 September the cabinet dismissed Count Detlev von Einsiedel, followed by Bernhard von Lindenau.
Therefore, it works as a neutron reflector and neutron moderator, effectively slowing the neutrons to the thermal energy range of below 0. 03 eV, where the total cross section is at least an order of magnitude lower – exact value strongly depends on the purity and size of the crystallites in the material.
Therefore, a base on balls does not increase nor decrease a player's batting average, but it does increase his on-base percentage, unless a player's on-base percentage is 1. 000, in which case it remains the same.
Therefore, when a runner on first or second base tags on a fly ball and advances no further than third base, no sacrifice is given and the batter is charged with an at-bat.
Therefore, unbeknown to the French who remained oblivious to the Allies ’ real strength and intentions on the opposite side of the Petite Gheete, Marlborough was throwing his full weight against Ramillies and the open plain to the south.
Therefore, biological agents may be useful as strategic deterrents in addition to their utility as offensive weapons on the battlefield.
Therefore hit points ( which increase with experience in D & D ) were based on the average of Size and Constitution and were functionally static for the life of the character.
" Therefore I should infer from analogy that probably all the organic beings which have ever lived on this earth have descended from some one primordial form, into which life was first breathed.
Therefore, while the basic features of this epoch have been worked out in the Big Bang theory, the details are largely based on educated guesses.
Therefore and group
Therefore, this group is generally now either included in the Brassicaceae or as its own family, Cleomaceae.
Therefore Latinos are Americans who are descendants of the Latin group ( namely Spain, France, Italy and Portugal ) and Hispanic refers to the descendants from the Iberian Peninsula ( also known as Ibero-American ).
Therefore, negative values of the group velocity will occur in these areas.
Therefore, one may alternatively define a group action of G on X as a group homomorphism from G into the symmetric group Sym ( X ) of all bijections from X to X.
Therefore, in addition to its strictly communicative uses, language also has many social and cultural uses, such as signifying group identity, social stratification, as well as for social grooming and entertainment.
Therefore, f induces a group homomorphism from the ( multiplicative ) group of units of R to the ( multiplicative ) group of units of S.
Therefore in 1863, the tribes from the area surrounding the middle Sacramento and Feather rivers, the Konkow group, were removed and marched forcibly to the Round Valley Indian Reservation near the Eel River.
Therefore its fundamental group H is free.
Therefore, in general Euclidean spaces every similarity is an affine transformation, because the Euclidean group E ( n ) is a subgroup of the affine group.
Therefore these arguments held that a group of people can join a government because it has the capacity to exercise a single will and make decisions with a single voice in the absence of sovereign authority — a notion rejected by Hobbes and later contract theorists.
Therefore group theoretic arguments underlie large parts of the theory of those entities.
) Therefore a subgroup of a group G is a subset S of G such that:
Therefore, according to its meaning in common usage in English, any given people, ethnic group or community may be described as being indigenous in reference to some particular region or location.
Therefore every finite simple group has even order unless it is cyclic of prime order.
Therefore, this group of compounds causes electrons to accumulate on chlorophyll molecules.
Therefore, in the context of Meyerhoff ’ s research, " eh " can be equated as a device to establish and maintain a group identity.
Therefore the existence and number of inner automorphisms that are not the identity mapping is a kind of measure of the failure of the commutative law in the group.
Therefore, it has the formula RCO -, where R represents an alkyl group that is attached to the CO group with a single bond.
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