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1 group duality
Математика: групповая двойственность -
2 group duality
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3 duality
1) взаимность2) двойственность, дуальность3) двойственное или дуальное отображение•duality on plane — матем. двойственность на плоскости
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4 групповая двойственность
group duality мат.Русско-английский научно-технический словарь Масловского > групповая двойственность
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5 групповая двойственность
Большой англо-русский и русско-английский словарь > групповая двойственность
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6 групповая двойственность
Mathematics: group dualityУниверсальный русско-английский словарь > групповая двойственность
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7 ingenuo
adj.ingenuous, as innocent as a lamb, artless, childlike.* * *► adjetivo1 naive, ingenuous► nombre masculino,nombre femenino1 naive person* * *(f. - ingenua)adj.* * *ADJ naïve, ingenuous* * *I- nua adjetivo naive, ingenuousII- nua masculino, femenino* * *= ingenuous, naive [naïve], innocent, simple-minded, gullible, born yesterday, guileless, clueless, corn-fed, unwordly.Ex. She put her empty cup in the dirty-dish cart, and mounted on the wings of a pure and ingenuous elation the long flight of stairs leading to the offices on the first floor.Ex. At the risk of sounding trite and a bit naive, I'd like to remind this group that the ISBD was also called, not for the cataloger's benefit, but as an international tool of bibliographic description.Ex. This is highly embarrassing for the innocent reader and for the apologetic library staff.Ex. Granted the seemingly simple-minded examples that have been used, such as changing NEGROES to AFRO-AMERICANS and BLACKS, appear fairly straightforward.Ex. I argue that intellectual vices (such as being gullible, dogmatic, pigheaded, or prejudiced) are essential.Ex. The article is entitled ' Born yesterday and other forms of original sin: two perspectives on library research'.Ex. He cites, for example, a popular reference book from the 1880s, which gushes about the Eskimo's guileless character, keen intelligence, and harmonious politics.Ex. This is largely clueless enthusiasm focused on things that don't matter in the grand scheme of things.Ex. The Wizard, played by Joel Grey, is a smooth-talking dumbbell who admits he is 'a corn-fed hick' and 'one of your dime-a-dozen mediocrities'.Ex. There exist sets of duality in this philosophy; body versus soul, worldly versus unworldly and life versus salvation.----* ingenuos, los = gullible, the.* * *I- nua adjetivo naive, ingenuousII- nua masculino, femenino* * *= ingenuous, naive [naïve], innocent, simple-minded, gullible, born yesterday, guileless, clueless, corn-fed, unwordly.Ex: She put her empty cup in the dirty-dish cart, and mounted on the wings of a pure and ingenuous elation the long flight of stairs leading to the offices on the first floor.
Ex: At the risk of sounding trite and a bit naive, I'd like to remind this group that the ISBD was also called, not for the cataloger's benefit, but as an international tool of bibliographic description.Ex: This is highly embarrassing for the innocent reader and for the apologetic library staff.Ex: Granted the seemingly simple-minded examples that have been used, such as changing NEGROES to AFRO-AMERICANS and BLACKS, appear fairly straightforward.Ex: I argue that intellectual vices (such as being gullible, dogmatic, pigheaded, or prejudiced) are essential.Ex: The article is entitled ' Born yesterday and other forms of original sin: two perspectives on library research'.Ex: He cites, for example, a popular reference book from the 1880s, which gushes about the Eskimo's guileless character, keen intelligence, and harmonious politics.Ex: This is largely clueless enthusiasm focused on things that don't matter in the grand scheme of things.Ex: The Wizard, played by Joel Grey, is a smooth-talking dumbbell who admits he is 'a corn-fed hick' and 'one of your dime-a-dozen mediocrities'.Ex: There exist sets of duality in this philosophy; body versus soul, worldly versus unworldly and life versus salvation.* ingenuos, los = gullible, the.* * *naive, ingenuous¡qué ingenuo eres! you're so naive!masculine, femininees un ingenuo ¿cómo se ha podido creer eso? he's so naive, how could he possibly have believed that?* * *
ingenuo◊ - nua adjetivo
naive, ingenuous
■ sustantivo masculino, femenino: es un ingenuo he's so naive
ingenuo,-a
I adjetivo naive
II sustantivo masculino y femenino naive person: es un ingenuo, he's so naive
' ingenuo' also found in these entries:
Spanish:
bobalicón
- bobalicona
- incauta
- incauto
- infeliz
- ingenua
- inocente
- prima
- primo
- simple
- pavo
- pueril
- tonto
English:
deluded
- dupe
- green
- ingenuous
- naive
- simple
- simple-minded
- unsophisticated
- childlike
* * *ingenuo, -a♦ adjnaive, ingenuous;¡no seas ingenuo! don't be so naive!♦ nm,fingenuous o naive person;es un ingenuo he's (very) naive;hacerse el ingenuo to act the innocent* * *I adj naiveII m, ingenua f naive person, sucker fam* * *cándido: naive♦ ingenuamente adv: naive person* * *ingenuo adj naive -
8 topological
топологический base of topological space ≈ база топологического пространства basis of topological space ≈ базис топологического пространства category of topological space ≈ категория топологического пространства dual topological unitarization ≈ дуально топологическая унитаризация general topological space ≈ общетопологическое пространство hyperemetric topological group ≈ гиперметрическая топологическая группа hypermetric topological group ≈ гиперметрическая топологическая группа linearly topological algebra ≈ линейно топологическая алгебра local topological structure ≈ локальная топологическая структура topological direct integral ≈ топологический прямой интеграл topological direct summand ≈ топологическое прямое слагаемое topological field of sets ≈ топологическое тело множеств topological group extension ≈ топологическое расширение группы topological spectral value ≈ топологическое спектральное значение topological vector lattice ≈ топологическая векторная решетка - topological conjugacy - topological contractibility - topological convergence - topological correspondence - topological covering - topological decomposition - topological deformation - topological dimension - topological distribution - topological divisor - topological dual - topological duality - topological dynamics - topological embedding - topological entropy - topological equivalence - topological equivalent - topological field - topological flow - topological formula - topological formulation - topological game - topological genus - topological graph - topological group - topological groupoid - topological homeomorphism - topological homogeneity - topological homomorphism - topological identification - topological image - topological inclusion - topological index - topological interpretation - topological invariance - topological invariant - topological irreducibility - topological isomorphism - topological knot - topological lattice - topological limit - topological line - topological logic - topological manifold - topological method - topological model - topological modification - topological module - topological monoid - topological morphism - topological neighborhood - topological nilpotent - topological noise - topological object - topological ordering - topological pair - topological partition - topological plane - topological polygon - topological polyhedron - topological polynomial - topological product - topological proof - topological property - topological pseudoisotopy - topological quasicomponent - topological quotient - topological rank - topological realization - topological recurrence - topological relationship - topological representation - topological restriction - topological result - topological ring - topological section - topological self-mapping - topological semigroup - topological semimodule - topological sequence - topological similarity - topological simplex - topological sorting - topological space - topological sphere - topological stability - topological structure - topological subgroup - topological subspace - topological substitute - topological sum - topological supplement - topological surface - topological transformation - topological transitivity - topological tree - topological triangle - topological type - topological uniformization - topological weight (математика) топологическийБольшой англо-русский и русско-английский словарь > topological
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9 space
1) интервал, промежуток2) пробел || оставлять пробелы3) область; площадь4) пространство || пространственный5) космос, космическое пространство6) полость7) расстояние•- absolutely compact space - absolutely embedded space - absolutely thick space - algebraically parallel space - almost complex space - almost expandable space - almost isomorphic space - almost metric space - almost nonsingular space - almost paracompact space - almost pretopological space - analytically ramified covering space - arcwise connected space - centrally harmonic space - compactly ordered space - completely continuous space - completely degenerate space - completely disconnected space - completely harmonic space - completely metric space - completely normal space - completely reducible space - completely regular space - completely reticulated space - completely separable space - completely separated space - completely symmetric space - completely uniformizable space - constant curvature space - continuous sample space - continuously ordered space - contractible in itself space - countably compactifiable space - countably dimensional space - countably generated space - countably infinite space - countably metacompact space - countably multinormed space - countably normed space - countably paracompact space - countably refinable space - countably subcompact space - finitely productive space - finitely sheeted space - finitely triangulated space - fully normal space - general metrizable space - general topological space - global analytic space - globally symmetric space - hereditarily normal space - hereditarily paracompact space - hereditarily separable space - hereditarily symmetric space - holomorphic tangent space - holomorphically complete space - holomorphically convex space - homotopy associative space - iterated loop space - linearly connected space - linearly ordered space - linearly topologized space - load space - locally bounded space - locally closed space - locally compact space - locally complete space - locally connected space - locally contractible space - locally convex space - locally directed space - locally fine space - locally holomorphic space - locally homogeneous space - locally hyperbolic space - locally linear space - locally metrizable space - locally ringed space - locally separable space - locally simply connected space - locally solid space - locally spherical space - locally star-shaped space - locally symmetric space - locally timelike space - locally triangulable space - monotonically normal space - naturally isomorphic space - naturally ordered space - naturally reductive space - nearly paracompact space - negative metric space - normally separated space - not simply connected space - nowhere connected space - null space of linear transformation - n-way projective space - perfectly normal space - perfectly regular space - perfectly screenable space - perfectly separable space - peripherically bicompact space - peripherically compact space - pointwise paracompact space - projectively metric space - quaternion hyperbolic space - quaternion projective space - quaternion vector space - regularly ordered space - relatively discrete space - relatively strong space - sequentially closed space - sequentially compact space - sequentially complete space - sequentially quasicomplete space - sequentially separable space - simply ordered space - simply partitionable space - space of affine connectedness - space of complex homomorphisms - space of continuous functions - space of finite measure - space of linear interpolation - space of right cosets - space of scalar curvature - strongly bounded space - strongly closed space - strongly compact space - strongly complete space - strongly irreducible space - strongly normal space - strongly normed space - strongly paracompact space - strongly pseudocompact space - strongly pseudometrizable space - strongly rigid space - strongly screenable space - structural space - structure space - topologically complete space - totally disconnected space - totally geodesic space - totally imperfect space - totally normal space - totally orderable space - totally ordered space - water jacket space - weakly closed space - weakly compact space - weakly complete space - weakly covering space - weakly dense space - weakly favorable space - weakly n-dimensional space - weakly paracompact space - weakly regular space - weakly separable space - weakly symmetric spaceto space out — полигр. набирать вразрядку
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10 bounded
1) граничить
2) ограниченный
3) ограниченно
4) разграниченный
5) связанный ∙ absolutely bounded form ≈ абсолютно ограниченная форма absolutely bounded function ≈ ограниченная по абсолютной величине функция absolutely bounded matrix ≈ абсолютно ограниченная матрица algebra of bounded representation type ≈ алгебра с ограниченными степенями представлений algebra of linearly bounded degree ≈ алгебра линейно ограниченной степени almost bounded function ≈ функция, ограниченная почти всюду bounded above function ≈ ограниченная сверху функция bounded above operator ≈ ограниченый сверху оператор bounded above subset ≈ ограниченное сверху подмножество bounded below function ≈ ограниченная снизу функция bounded below operator ≈ ограниченный снизу оператор bounded below subset ≈ ограниченное снизу подмножество bounded closed interval ≈ ограниченный замкнутый интервал bounded distance decoding ≈ декодирование с ограниченным расстоянием bounded from one side ≈ полуограниченный bounded open interval ≈ ограниченный открытый интервал bounded partial quotient ≈ ограниченное неполное частное bounded pure subgroup ≈ ограниченная сервантная подгруппа bounded random variable ≈ ограниченная случайная величина bounded universal hypothesis ≈ ограниченная универсальная гипотеза bounded variable technique ≈ метод ограниченной переменной collectively bounded set ≈ ограниченное в совокупности множество completely bounded set ≈ вполне ограниченное множество completely bounded space ≈ вполне органическое пространство completely bounded statistic ≈ вполне ограниченная статистика derivative of bounded variation ≈ производная с ограниченной вариацией doubly bounded quantifier ≈ ограниченный с двух сторон квантор essentially bounded function ≈ существенно ограниченная функция essentially bounded random variable ≈ существенно ограниченная случайная величина essentially bounded sequence ≈ существенно ограниченная последовательность explicitly bounded function ≈ явно ограниченная функция finitely bounded germ ≈ конечно ограниченный росток function of bounded characteristic ≈ функция с ограниченной характеристикой function of bounded type ≈ функция ограниченного вида function of bounded variation ≈ функция с ограниченным изменением linearly bounded automaton ≈ линейно ориентированный автомат linearly bounded set ≈ линейно ограниченное множество locally bounded curvature ≈ локально ограниченная кривизна locally bounded density ≈ локально ограниченная плотность locally bounded function ≈ локально ограниченная функция locally bounded game ≈ локально ограниченная игра locally bounded space ≈ локально ограниченное пространство metrically bounded functional ≈ метрически ограниченный функционал metrically bounded set ≈ метрически ограниченное множество nontangentially bounded function ≈ нетангенциально ограниченная функция nontangentially bounded integral ≈ некасательно ограниченный интеграл order bounded functional ≈ ограниченный по упорядоченности функционал pointwise bounded function ≈ точечно ограниченная функция polynomially bounded function ≈ полиномиально ограниченная функция process with bounded aftereffect ≈ процесс с ограниченным последействием progressively bounded graph ≈ прогрессивно ограниченный граф recursively bounded quantifier ≈ рекурсивно ограниченный квантор regressively bounded graph ≈ регрессивно ограниченный граф relatively bounded form ≈ относительно ограниченная форма sequentially bounded net ≈ последовательно ограниченная сеть simply bounded subset ≈ поточечно ограниченное подмножество smoothly bounded region ≈ гладко ограниченная область stochastically bounded sequence ≈ стохастически ограниченная последовательность strictly bounded set ≈ строго ограниченное множество strongly bounded set ≈ сильно ограниченное множество strongly bounded space ≈ сильно ограниченное пространство theor of semigroups of linear bounded operators ≈ теория полугрупп линейных ограниченных операторов topology of bounded convergence ≈ топология ограниченной сходимости totally bounded measure ≈ вполне ограниченная мера totally bounded set ≈ вполне ограниченное множество totally bounded space ≈ вполне ограниченное пространство totally bounded subset ≈ вполне ограниченное подмножество totally bounded uniformity ≈ вполне ограниченная равномерность uniformly bounded convergence ≈ равномерно ограниченная сходимость uniformly bounded curvature ≈ равномерно ограниченная кривизна uniformly bounded error ≈ равномерно ограниченная ошибка uniformly bounded family ≈ равномерно ограниченное семейство uniformly bounded function ≈ равномерно ограниченная функция uniformly bounded kernel ≈ равномерно ограниченное ядро uniformly bounded sequence ≈ равномерно ограниченная последовательность uniformly bounded series ≈ равномерно ограниченный ряд uniformly bounded set ≈ равномерно ограниченное множество uniformly bounded variation ≈ равномерно ограниченная вариация weakly bounded set ≈ слабо ограниченное множество weakly bounded subset ≈ слабо ограниченное подмножество - almost bounded - bounded above - bounded acceptor - bounded accuracy - bounded adele - bounded aggregate - bounded approximation - bounded automaton - bounded axonometry - bounded below - bounded characteristic - bounded collection - bounded compactness - bounded completeness - bounded continuum - bounded convergence - bounded curvature - bounded decomposition - bounded deficiency - bounded degree - bounded derivation - bounded derivative - bounded deviation - bounded difference - bounded distribution - bounded domain - bounded duality - bounded extension - bounded field - bounded flow - bounded form - bounded frontier - bounded function - bounded functional - bounded group - bounded homomorphism - bounded index - bounded integral - bounded integrand - bounded intersection - bounded invertibility - bounded kernel - bounded language - bounded lattice - bounded mapping - bounded martingale - bounded matrix - bounded measure - bounded metric - bounded module - bounded monotonicity - bounded morphism - bounded motion - bounded network - bounded norm - bounded operator - bounded order - bounded path - bounded polyhedron - bounded potential - bounded predicate - bounded problem - bounded product - bounded projection - bounded quality - bounded quantification - bounded quantifier - bounded quantity - bounded quotient - bounded region - bounded representation - bounded retract - bounded semigroup - bounded sequence - bounded series - bounded set - bounded solution - bounded space - bounded spectrum - bounded spline - bounded string - bounded subset - bounded subtraction - bounded sum - bounded summand - bounded support - bounded term - bounded topology - bounded transformation - bounded utility - bounded variance - bounded variation - bounded varying - bounded vector - essentially bounded - explicitly bounded - exponentially bounded - power bounded - uniformly bounded - weakly bounded (математика) ограниченный -
11 theory
1) теория
2) <phys.> борновский
3) учение
4) толкование
5) трактовка
6) истолкование
– abandon theory
– accept theory
– acid-base theory
– advance theory
– airfoil theory
– atomic theory
– band theory
– Bardeen-Cooper-Schrieffer theory
– BCS theory
– circuit theory
– classical theory
– collision theory
– combinatorial theory
– communication theory
– control theory
– deductive theory
– dimensional theory
– dislocation theory
– duality theory
– field theory
– formal theory
– gage theory
– Gersho-Rosencwaig theory
– graph theory
– group theory
– ideal theory
– impact theory
– in theory
– informal theory
– information theory
– measure theory
– object theory
– percolation theory
– pertubation theory
– perturbation theory
– probability theory
– proof theory
– quantum theory
– queueing theory
– queuing theory
– ray theory
– reject theory
– relativity theory
– reliability theory
– residue theory
– rigorous theory
– scheduling theory
– second-order theory
– set theory
– shower theory
– similarity theory
– stability theory
– switching-circuit theory
– theory of correspondence
– theory of elasticity
– theory of estimation
– theory of games
– theory of probability
– theory of queues
– theory of relativity
– theory of sampling
– theory of solids
– theory of valuations
– transport theory
additive ideal theory — <math.> теория идеалов аддитивная
barrier theory of cyclogenesis — <meteor.> теория циклогенеза заслоночная
general theory of relativity — <phys.> теория относительности общая
grand unification theory — <phys.> модель большого объединения, модель великого объединения
unified field theory — <phys.> теория поля единая, теория поля обобщенная
Yukawa meson theory — <phys.> теория мезонная юкавская
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12 теория
analysis, science, theory* * *тео́рия ж.
theoryвыдвига́ть тео́рию — advance [propose] a theoryобъясня́ть что-л. на основа́нии тео́рии — explain smth. on a theoryотказа́ться от тео́рии — abandon a theoryотклоня́ть тео́рию — reject a theoryподтвержда́ть тео́рию эксперимента́льно — verify a theory by experimentпринима́ть [признава́ть] тео́рию — accept a theoryтео́рия автомоде́льности — similarity theoryтео́рия адсо́рбции Бруна́уэра—Эмме́тта—Те́ллера — BET theory of adsorptionтео́рия Ба́рдина—Ку́пера—Шри́ффера [БКШ] — Bardeen-Cooper-Schrieffer [BCS] theoryтео́рия больши́х сигна́лов — large signal theoryтео́рия бу́левых а́лгебр — Boolean calculusтео́рия вероя́тностей — theory of probability, probability theoryтео́рия Ви́нера — prediction theoryтео́рия возмуще́ний мат. — perturbation theoryтео́рия второ́го приближе́ния — second-order theoryтео́рия вы́борочного ме́тода стат. ( не путать с отсчё́тами в теории сообщений) — theory of samplingтео́рия вы́четов — residue theoryтео́рия гра́фов мат. — graph theoryтео́рия групп мат. — group theory, theory of groupsтео́рия дво́йственности — duality theoryтео́рия доказа́тельства — proof theoryтео́рия Друде́—Ло́ренца элк. — Drude-Lorentz theoryтео́рия игр мат. — theory of games, game(s) theoryтео́рия информа́ции — general theory of communication, information theoryква́нтовая тео́рия — quantum theoryтео́рия кисло́т и основа́ний — acid-base theoryкласси́ческая тео́рия — classical theoryтео́рия крыла́ — airfoil theoryлучева́я тео́рия — ray theoryтео́рия ма́лых сигна́лов — small signal theoryтео́рия ма́ссового обслу́живания — queueing [waiting-line] theoryтео́рия ме́ры мат. — measure theoryтео́рия мно́жеств — set theoryтео́рия надё́жности — reliability theoryтео́рия наибо́льших деформа́ций — ultimate strain theoryтео́рия относи́тельности — theory of relativityтео́рия относи́тельности, о́бщая — general theory of relativity, general relativityтео́рия относи́тельности, специа́льная — special theory of relativityтео́рия очереде́й — queueing [waiting-line] theoryтео́рия оши́бок — error analysisтео́рия перено́са — transport theoryтео́рия подо́бия — similarity theoryтео́рия по́ля — field theoryтео́рия разме́рностей — dimensional theoryтео́рия регули́рования — control theoryтео́рия реле́йных схем — switching-circuit theoryтео́рия све́та, волнова́я — wave theory of lightтео́рия све́та, ква́нтовая — quantum theory of lightтео́рия све́та, корпускуля́рная — corpuscular theory of lightтео́рия соедине́ний — combinatorial mathematics, combinatoricsтео́рия сравне́ний — congruence theoryтео́рия статисти́ческих оце́нок — theory of estimationтео́рия столкнове́ний — collision theoryстро́гая тео́рия — rigorous theoryтео́рия твё́рдых тел, зо́нная — band theory of solidsтео́рия теплопереда́чи — heat-transfer theoryтео́рия управле́ния — control theoryтео́рия упру́гости — theory of elasticityтео́рия усто́йчивости — stability theoryфеноменологи́ческая тео́рия — phenomenological [formal] theoryформа́льная тео́рия — formal theoryтео́рия цве́тности — theory of colour valueтео́рия цепе́й — circuit [network] theoryтео́рия чи́сел — theory of numbers, number theory -
13 wave
nACOUST, ELEC onda fELEC ENG onda f, onda de baja frecuencia fPHYS, TELECOM, WATER TRANSP, WAVE PHYS onda f -
14 homomorphism
гомоморфизм, гомоморфное отображение- locally nilpotent homomorphism - locally rigid homomorphism - lower complete homomorphism - lower semicomplete homomorphism - monic homomorphism - retractive homomorphism -
15 isomorphism
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16 law
1) закон3) правило4) принцип•under the law — по закону, согласно закону, в соответствии с законом
- Biot law- converse law of double negation- cube law- distributive law of disjunction over conjunction - double law of the mean - fifth power law - first distributive law - first law of mean- gas law- idempotency law - infinitely decomposable law - infinitely divisible law - inverse sine law - inverse square law - law of addition of probability - law of alteration of quantifiers - law of associativity of disjunction - law of comparative judgment - law of constant angles - law of double complementation - law of equal significance - law of mass action - law of random function - law of random vector - law of requisite variety - law of right invertibility - law of statistical regularity - law of universal causation - law of universal gravitation - Newton's first law of motion - Newton's law of gravitation - Newton's second law of motion - Newton's third law of motion - normal law of composition - normal law of errors - one-sided modular law - probabilistic law - probability law - product law of probability - quadratic reciprocity law - second law of mean - second order law - similitude law- time law- weak law -
17 theory
1) теория; учение2) толкование; трактовка3) теоретическое объяснение; теоретические основы•- band theory of solids - corpuscular theory of light - general theory of relativity - strongly undecidable theory - wave theory of light - Yukawa meson theory
См. также в других словарях:
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Pontryagin duality — In mathematics, in particular in harmonic analysis and the theory of topological groups, Pontryagin duality explains the general properties of the Fourier transform. It places in a unified context a number of observations about functions on the… … Wikipedia
Tannaka–Krein duality — In mathematics, Tannaka–Krein duality theory concerns the interaction of a compact topological group and its category of linear representations. Its natural extension to the non Abelian case is the Grothendieck duality theory. It extends an… … Wikipedia
Tannaka-Krein duality — In mathematics, Tannaka Krein duality theory concerns the interaction of a compact topological group and its category of linear representations. It extends an important mathematical duality between compact and discrete commutative topological… … Wikipedia
Poincaré duality — In mathematics, the Poincaré duality theorem, named after Henri Poincaré, is a basic result on the structure of the homology and cohomology groups of manifolds. It states that if M is an n dimensional compact oriented manifold, then the k th… … Wikipedia
S-duality — In theoretical physics, S duality (also a strong weak duality) is an equivalence of two quantum field theories, string theories, or M theory. An S duality transformation maps the states and vacua with coupling constant g in one theory to states… … Wikipedia
Compact group — In mathematics, a compact (topological, often understood) group is a topological group whose topology is compact. Compact groups are a natural generalisation of finite groups with the discrete topology and have properties that carry over in… … Wikipedia
Alvis–Curtis duality — In mathematics, Alvis–Curtis duality is a duality operation on the characters of a reductive group over a finite field, introduced by Charles W. Curtis (1980) and studied by his student Dean Alvis (1979). Kawanaka (1981, 1982)… … Wikipedia
