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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 .
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]
In geometry, the hinge theorem (sometimes called the open mouth theorem) states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle. [1]
In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal. It is Proposition 35 of Book 3 of Euclid's Elements.
The orange and green quadrilaterals are congruent; the blue is not congruent to them. All three have the same perimeter and area. (The ordering of the sides of the blue quadrilateral is "mixed" which results in two of the interior angles and one of the diagonals not being congruent.)
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 .
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 ...
In mathematics, a structure on a set (or on some sets) refers to providing it (or them) with certain additional features (e.g. an operation, relation, metric, or topology). Τhe additional features are attached or related to the set (or to the sets), so as to provide it (or them) with some additional meaning or significance.