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Geometric join of two line segments.The original spaces are shown in green and blue. The join is a three-dimensional solid, a disphenoid, in gray.. In topology, a field of mathematics, the join of two topological spaces and , often denoted by or , is a topological space formed by taking the disjoint union of the two spaces, and attaching line segments joining every point in to every point in .
Castelnuovo–de Franchis theorem (algebraic geometry) Chow's theorem (algebraic geometry) Cramer's theorem (algebraic curves) (analytic geometry) Hartogs's theorem (complex analysis) Hartogs's extension theorem (several complex variables) Hirzebruch–Riemann–Roch theorem (complex manifolds) Kawamata–Viehweg vanishing theorem (algebraic ...
Geometry (from Ancient Greek γεωμετρία (geōmetría) 'land measurement'; from γῆ (gê) 'earth, land' and μέτρον (métron) 'a measure') [1] is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. [2]
In algebraic geometry, given irreducible subvarieties V, W of a projective space P n, the ruled join of V and W is the union of all lines from V to W in P 2n+1, where V, W are embedded into P 2n+1 so that the last (resp. first) n + 1 coordinates on V (resp. W) vanish. [1]
A term's definition may require additional properties that are not listed in this table. This Hasse diagram depicts a partially ordered set with four elements: a , b , the maximal element a ∨ {\displaystyle \vee } b equal to the join of a and b , and the minimal element a ∧ {\displaystyle \wedge } b equal to the meet of a and b .
The statement is often used as a justification in elementary geometry proofs when a conclusion of the congruence of parts of two triangles is needed after the congruence of the triangles has been established.
A geometry: it is equipped with a metric and is flat. A topology: there is a notion of open sets. There are interfaces among these: Its order and, independently, its metric structure induce its topology. Its order and algebraic structure make it into an ordered field.
In mathematics, the term adjoint applies in several situations. Several of these share a similar formalism: if A is adjoint to B, then there is typically some formula of the type (Ax, y) = (x, By). Specifically, adjoint or adjunction may mean: Adjoint of a linear map, also called its transpose in case of matrices