From an algebraic point of view, the set of holomorphic functions on an open set is a commutative ring and a complex vector space.

From about the 1920s onwards, it was realised that tensors play a basic role in algebraic topology ( for example in the Künneth theorem ).

From the point of view of universal algebra, an algebra ( or algebraic structure ) is a set A together with a collection of operations on A.

From an algebraic point of view, if D is connected, then the set of meromorphic functions is the field of fractions of the integral domain of the set of holomorphic functions.

From the point of view of Lie theory, the classical unitary group is a real form of the Steinberg group, which is an algebraic group that arises from the combination of the diagram automorphism of the general linear group ( reversing the Dynkin diagram A < sub > n </ sub >, which corresponds to transpose inverse ) and the field automorphism of the extension C / R ( namely complex conjugation ).

From this proof get the algebraic statement:

From a very young age he was an outstanding figure in the school of Henri Cartan, working on algebraic topology, several complex variables and then commutative algebra and algebraic geometry, in the context of sheaf theory and homological algebra techniques.

From about 1950 to 1980 there was considerable effort to salvage as much as possible from the wreckage, and convert it into the rigorous algebraic style of algebraic geometry set up by Weil and Zariski.

From the monotonicity and continuity of relation composition, it follows immediately that the set of the bisimulations is closed under unions ( joins in the poset of relations ), and a simple algebraic calculation shows that the relation of bisimilarity — the join of all bisimulations — is an equivalence relation.

From an algebraic viewpoint, this means that one wants to find adequate notions of homomorphisms for the structures under consideration.

From the Grothendieck point of view, motives should further contain the information provided by algebraic de Rham cohomology, and crystalline cohomology.

From an algebraic perspective, complex numbers enter quite naturally into the study of algebraic functions.

From an algebraic perspective, a semigroup action is a generalization of the notion of a group action in group theory.

Arnold later returned to the question, jointly with Goro Shimura ( V. I. Arnold and G. Shimura, Superposition of algebraic functions ( 1976 ), in Mathematical Developments Arising From Hilbert's Problems ).

One, a reservation on the point I have just made, is the phenomenon of pseudo-thinking, pseudo-feeling, and pseudo-willing, which Fromm discussed in The Escape From Freedom.

From the point of view of popularity the best-known member of the Commission was Walter Camp, the Yale athlete whose sobriquet was `` the father of American football ''.

From this point of view the `` militant mobs '' of the past, stirred into action by one ideology or another, were all composed of `` intellectuals '' -- and this is not the level on which the essence of mankind can be discovered.

From the moment of the occupation Lublin became a focal point.

From this point, I paint in as direct a manner as possible, by flowing on the washes with as pure a color mixture as I can manage.

From the manufacturer's point of view, the increasing cost of advertising and promotion is a very real problem to be faced in the sixties.

From the point of view of the applicants, less time was wasted in being evaluated -- and they got a meal out of it as well as some insights into their performances.

From the point of view of syntactic analysis the head word in the statement is the predicator has broken, and from the point of view of meaning it would seem that the trouble centers in the breaking ; ;

From the point of view of word formation real might be expected to have two syllables.

From the rather tortuous history of electoral planning in Morocco an important point emerges concerning the first elections in a developing country and evaluating their results.

From that point on he said he went to the post office and then walked leisurely to where his niece was staying, more than a mile away.

From the lioness' point of view, this strange creature on the back of another creature, lashing out with its long thin paw, very likely appeared as something she could not at first cope with.

From an economic point of view, the order Asparagales is second in importance within the monocots to the order Poales ( which includes grasses and cereals ).

From this point on he establishes himself as a psychological detective who proceeds not by a painstaking examination of the crime scene, but by enquiring either into the nature of the victim or the psychology of the murderer.

From this point, his mother and stepfather took a more active role in raising him.

From an artistic point of view, he was most successful in portrait-statues and groups of children, where he was obliged to follow nature most closely.

From the most northerly point, Ras ben Sakka in Tunisia, in 37 ° 21 ′ N, to the most southerly point, Cape Agulhas in South Africa, 34 ° 51 ′ 15 ″ S, is a distance approximately of ; from Cape Verde, 17 ° 33 ′ 22 ″ W, the westernmost point, to Ras Hafun in Somalia, 51 ° 27 ′ 52 ″ E, the most easterly projection, is a distance ( also approximately ) of.

From a strictly aerodynamic point of view, the term should refer only to those side-effects arising as a result of the changes in airflow from an incompressible fluid ( similar in effect to water ) to a compressible fluid ( acting as a gas ) as the speed of sound is approached.

From that point on, the show was a success.

From a political point of view, there is a trade-off between Bulgaria's economic growth and the stability required for early accession to the monetary union.

From a philosophical point of view, what makes the brain special in comparison to other organs is that it forms the physical structure that generates the mind.

From south to north, Broadway at one point or another runs over or under the IRT Lexington Avenue Line, the BMT Broadway Line, the IRT Broadway – Seventh Avenue Line, and the IND Eighth Avenue Line:

File: View From the Ponte Vecchio of the River Arno. jpg | The view of the Arno from the Ponte Vecchio

From a strategic point of view, the Athenians had some disadvantages at Marathon.

From a bibliographical point of view some of the early printed Breviaries are among the rarest of literary curiosities, being merely local.

From the local point of view time stops at the horizon, whereas from the global point of view time extends beyond it, and surfaces of constant time cross the horizon.

From the point of view of State-centric law, extraordinary procedures ( usually international courts ) may prosecute such crimes.

From the peak's platform the panoramic view includes downtown Rio, Sugarloaf Mountain, the Lagoa Rodrigo de Freitas ( lake ), Copacabana and Ipanema beaches, Estádio do Maracanã ( Maracanã Stadium ), and several of Rio's favelas.

From an architectural point of view, this arrangement could provide better floor area utilisation, offering an internal column-free office area with a clear depth of 9 to 13. 4 metres and an overall usable floor area efficiency of 81 %.

From a geometrical point of view, looking at the states of each variable of the system to be controlled, every " bad " state of these variables must be controllable and observable to ensure a good behaviour in the closed-loop system.

From the view of the citizens, these vicars were cruel and petty.

From a linguistic point of view, Bokmål and Danish are the same language.

From the point of view of differential topology, the donut and the coffee cup are the same ( in a sense ).