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theorem of duality

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  • Duality (projective geometry) — A striking feature of projective planes is the symmetry of the roles played by points and lines in the definitions and theorems, and (plane) duality is the formalization of this metamathematical concept. There are two approaches to the subject of …   Wikipedia

  • Duality theory for distributive lattices — In mathematics, duality theory for distributive lattices provides three different (but closely related) representations of bounded distributive lattices via Priestley spaces, spectral spaces, and pairwise Stone spaces. This generalizes the well… …   Wikipedia

  • Duality (mathematics) — In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one to one fashion, often (but not always) by means of an involution operation: if the dual… …   Wikipedia

  • Duality (electrical circuits) — For other meanings of the word not related to electrical circuits, see Duality (disambiguation). In electrical engineering, electrical terms are associated into pairs called duals. A dual of a relationship is formed by interchanging voltage and… …   Wikipedia

  • duality — /dooh al i tee, dyooh /, n. 1. a dual state or quality. 2. Math. a symmetry within a mathematical system such that a theorem remains valid if certain objects, relations, or operations are interchanged, as the interchange of points and lines in a… …   Universalium

  • Duality (order theory) — In the mathematical area of order theory, every partially ordered set P gives rise to a dual (or opposite) partially ordered set which is often denoted by Pop or Pd. This dual order Pop is defined to be the set with the inverse order, i.e. x ≤ y… …   Wikipedia

  • 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

  • Stone duality — In mathematics, there is an ample supply of categorical dualities between certain categories of topological spaces and categories of partially ordered sets. Today, these dualities are usually collected under the label Stone duality, since they… …   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

  • 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

  • Serre duality — In algebraic geometry, a branch of mathematics, Serre duality is a duality present on non singular projective algebraic varieties V of dimension n (and in greater generality for vector bundles and further, for coherent sheaves). It shows that a… …   Wikipedia

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