Duality (mathematics)

pair of transformation rules that are both valid rules of inference

vector space of linear functionals (may consist only on continuous functionals or of all functionals)

polyhedron whose vertices correspond to the faces of another one

involutive transformation on real-valued convex functions of one real variable

theorem

graph representing faces of another graph

duality for locally compact abelian groups

translates mathematical concepts into other concepts, in a one-to-one fashion

symmetry in projective geometry

duality that relates homology and cohomology groups for oriented closed manifolds

correspondence between properties of a category and its opposite

locally convex topological vector space that coincides with the continuous dual of its continuous dual space, both as linear space and as topological space

statement about integration of differential forms on manifolds

the ("dual") lower-semicontinuous convex function resulting from the Legendre–Fenchel transformation of a "primal" function

linear map from p-forms on an n-dimensional manifold to (n−p)-forms

Hyperplane in geometry

electrical circuits that are the dual of each other

equivalence relation on rings

dualities between elements or properties of electrical circuits, such as between voltage and current

equivalence between the derived Fukaya category of a symplectic manifold and the derived category of coherent sheaves on a complex manifold

dual pair of vector spaces

class of symmetries in string theory

statement about linear functionals and measures

algebraic encoding of graph connectivity

duality for holomorphic vector bundles on a compact complex manifold induced by a dualizing sheaf

duality of the homology of the complement of a subspace

mathematical conjecture