Indeed, it coincides with the topology of pointwise convergence of linear functionals.

Indeed, this follows since just as the image of a vector subspace under a linear transformation is a subspace, so is the image of V under L. But the only subspaces ( i. e., k-subspaces ) of k are

Indeed what was done is almost precisely to explain that tensor spaces are the constructions required to reduce multilinear problems to linear problems.

Indeed, the Future Value in this case grows linearly ( it's a linear function of the initial investment ): it doesn't take into account the fact that the interest earned might be compounded itself and produce further interest ( which corresponds to an exponential growth of the initial investment-see below -).

Indeed, fractional coloring problems are much more amenable to a linear programming approach than traditional coloring problems.

Indeed, area coordinates will also allow us to perform a linear interpolation at all points in the triangle if the values of the function are known at the vertices.

Indeed, if f: U → X is such a function and T: X → C a bounded linear functional, one can show that

Indeed, in the United States, cross-examination is seen as a core part of the entire adversarial system of justice, in that it " is the principal means by which the believability of a witness and the truth of his testimony are tested.

Indeed, the expert system quickly developed in front of the expert shows him if the future application should be programmed.

Indeed, in these countries, a jury trial is seen as a failing of some foreign legal system rather than an advantage ; this is despite the fact that both nations are common law countries.

Indeed, punishment of the obviously mentally ill by the state may act so as to undermine public confidence in the penal system.

Indeed, many advocates of STV argue that preventing nationwide proportionality is one of the primary goals of the system, to avoid the perceived risks of a fragmented legislature.

Indeed, critics of a specific syncretistic trend may sometimes use the word " syncretism " as a disparaging epithet, as a charge implying that those who seek to incorporate a new view, belief, or practice into a religious system actually distort the original faith.

Indeed, most states adopted one version or another of the system he established in Massachusetts, especially the program for " normal schools " to train professional teachers.

Indeed, neorealists often argue that the ordering principle of the international system has not fundamentally changed from the time of Thucydides to the advent of nuclear warfare.

Indeed, the region between them is a no-man's-land: attempts to bring the system to the midpoint of line-segment AB will result in a mixture of liquid A and vapor B, but nothing at the midpoint.

Indeed, in the early history of the Earth ( about four billion years ago ) bolide impacts were almost certainly common since the solar system contained far more discrete bodies than at present.

Indeed, after the ratification of the Constitution, some opponents of a strong federal judiciary urged that the federal court system be limited to the Supreme Court, which would hear appeals from state courts.

Indeed, according to the Gauge-gravity duality conjecture, all microscopic processes in a black hole are reversible, and only the collective behavior is irreversible, as in any other macroscopic, thermal system.

Indeed, this system was demonstrated to members of the Royal Society in London in 1926, which is generally recognised as being the first public demonstration of a true, working television system.

Indeed, most northern states adopted one version or another of the system he established in Massachusetts, especially the program for " normal schools " to train professional teachers.

The upshot is that the first fundamental form () is invariant under changes in the coordinate system, and that this follows exclusively from the transformation properties of E, F, and G. Indeed, by the chain rule,

Indeed Greg Johnson, StarFlight's lead designer, helped write dialog for Star Control II and Paul Reiche III contributed to the earlier game's alien communication system.

Indeed, Apple shipped such a diagnostic " operating system " in many Power Macintoshes.

Indeed, the remains of hilltop gardens, sculptures and a massive aqueduct system show the impressive engineering skills and aesthetic appreciation of his reign.

Indeed, the blood itself is essentially identical with the coelomic fluid that bathes the organs directly, and also fills the water vascular system.

Indeed, the world itself is an extremely old and sophisticated automated system.

Indeed, the laws of a legal system may be quite unjust, and the state may be quite illegitimate.

Indeed Luca Pacioli helped create the Banking system of the Italian city-states with his " double-entry bookkeeping ": his 27-page treatise on bookkeeping contained the first known published work on that topic, and is said to have laid the foundation for double-entry bookkeeping ( of Genoese merchants ) as it is practiced today.

Indeed, they would have been a formidable threat to Humanity, had they not been bottled up in their home system.

Indeed, for De Gaulle, the " regime of the parties " which characterized the parliamentary system, did not permit the advent of a strong and efficient state.

Indeed, in the largest biological weapons accident known – the anthrax outbreak in Sverdlovsk ( now Yekaterinburg ) in the Soviet Union in 1979, sheep became ill with anthrax as far as 200 kilometers from the release point of the organism from a military facility in the southeastern portion of the city ( known as Compound 19 and still off limits to visitors today, see Sverdlovsk Anthrax leak ).

Indeed, the format is ideally suited to such analysis because the viewer is afforded the opportunity to see how a person reacts on the outside through the constant recording of their actions and also what they feel on the inside through the Diary Room / Confession Room.

Indeed, many people have come to see the song as a life-affirming ode to optimism.

For one example, he expressed this playfulness in what is perhaps his most famous rhyme, a twist on Joyce Kilmer's verse: " I think that I shall never see / a poem lovely as a tree ", which drops " billboard " in place of poem and adds, " Indeed, unless the billboards fall / I'll never see a tree at all.

Indeed, some have described council communism as " socialism from below ," which they counterpose against what they see as the " socialism from above " that was endorsed by Stalinism.

Indeed, some centaurs undergo seasonal changes when they approach the Sun, making the boundary blurred ( see 2060 Chiron and 133P / Elst – Pizarro ).

Indeed, in the period immediately after his death, Mozart's reputation rose substantially: Solomon describes an " unprecedented wave of enthusiasm " for his work ; biographies were written ( first by Schlichtegroll, Niemetschek, and Nissen ; see Biographies of Mozart ); and publishers vied to produce complete editions of his works.

Indeed, some proponents of market socialism see the latter as a form of democratic socialism.

Indeed, in the largest biological weapons accident known – the anthrax outbreak in Sverdlovsk ( now Yekaterinburg ) in the Soviet Union in 1979, sheep became ill with anthrax as far as 200 kilometers from the release point of the organism from a military facility in the southeastern portion of the city ( known as Compound 19 and still off limits to visitors today, see Sverdlovsk Anthrax leak ).

Indeed, the geography of Riverdale is far too inconsistent for it to be any one specific location ( see below ).

Indeed, Adelina Patti and Luisa Tetrazzini were the only Italian sopranos to enjoy star status in London and New York in the late-Victorian and Edwardian eras, while such well-known compatriots and coevals of theirs as Gemma Bellincioni and Eugenia Burzio ( among several others ) failed to please Anglo-Saxon ears because, unlike Patti and Tetrazzini, they possessed unsteady, vibrato-laden voices — see Scott for evaluations of their respective techniques.

Indeed, at some Etruscan tombs, such as those of the Tumulus di Montefortini at Comeana ( see Carmignano ) in Tuscany, physical evidence of trade has been found in the form of grave goods — fine faience ware cups are particularly notable examples.

Indeed, Sir Toby in Twelfth Night is seen saying, in reference to Sir Andrew's hair, that " it hangs like flax on a distaff ; and I hope to see a housewife take thee between her legs and spin it off ;" the Nurse in Romeo and Juliet says that her husband had told Juliet when she was learning to walk that " Yea, dost thou fall upon thy face?

Indeed, it is not hard to see that it is equivalent to the Boolean prime ideal theorem ( BPIT ), a well-known intermediate point between the axioms of Zermelo-Fraenkel set theory ( ZF ) and the ZF theory augmented by the axiom of choice ( ZFC ).

Indeed the use of domes as a feature of Islamic architecture has gotten its roots from Roman Greater-Syria ( see Dome of the Rock ).

Indeed, critics have explored at length the parallels between Clamence's fall and Dante's descent through Hell in the Inferno ( see Galpin, King ).

Indeed, people have been stopped at airports solely due to their political views recently ( see No-fly list ) and there appears to be little public will to stop practices of this nature.

Indeed when the Mongols invaded the fortress, Juwayni was astonished to see stored countless supplies in perfect condition to withstand a possible siege.

Indeed, Seekers shunned creeds ( see Free Christianity ) and each assembly tended to embrace a broad spectrum of ideas.

Indeed, it is usually necessary to see several moves ahead in exact detail before launching a combination, or else the initial sacrifice would not be undertaken.

Indeed each incidence structure gives a spherical building of rank 2 ( see ); and Ballmann and Brin proved that every 2-dimensional simplicial complex in which the links of vertices are isomorphic to the flag complex of a finite projective plane has the structure of a building, not necessarily classical.

Indeed, it should not have been difficult to see how, among the Allied Powers, Italy had been the one which benefited the most from the outcome of the war.

Indeed, two elements of the room's decoration ( but not the amber panels themselves ) were eventually rediscovered ( see below ).

Indeed this happened when the negotiation with Symbolics ( see below ) was complete.