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Projective space

In mathematics, the concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet at infinity. A projective space may thus be viewed as the extension of a Euclidean space, or, more generally, an affine space with points at infinity, in such a way that there is one point at infinity of each direction of p…

Related concepts, Algebraic geometry & Definition

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Overview

Motivation

Definition

Related concepts

Topology

Algebraic geometry

Synthetic geometry

Morphisms

Dual projective space

Generalizations

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Map overview Semantic statistics

Projective space

Nodes180
Edges179
Triples183
Avg. degree1.99
Density0.011111
Components1

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Projective space

Top relations

related to References · 62
Projective space → Advanced Mathematics, Afanas'ev, Albrecht, Algebraic Geometry, An Introduction, Band, Berlin, Blaisdell Publishing Co, Cambridge Studies, Cambridge University Press, Chelsea, Co, Cohn-Vossen, Cole, Dover, EMS PressBaer, Encyclopedia, English, Ergebnisse, Euclidean
related to Classification · 12
Projective space → All, Desargues's, Desarguesian, Dimension, PG, The, The Desarguesian, There, These, Two, Veblen, Young
related to Finite projective spaces and planes · 10
Projective space → All, Desarguesian, For, GF, However, In, Notationally, PG, Up, Wedderburn's
related to Motivation · 10
Projective space → As, Cartesian, Mathematically, More, OP, P1, P2, Pinhole, Such, Then
related to Projective geometry · 10
Projective space → Again, Another, Euclidean, In, One, Properties, See Projective, The, This, Unlike
related to Algebraic geometry · 8
Projective space → Another, Bézout's, For, In, It, Originally, So, These
related to Definition · 8
Projective space → Given, If, In, Kn, KPn, Pn, The, This
related to Dual projective space · 8
Projective space → Chap, Grassmannian, II, In, One, See EGAII, That, When
related to Projective transformation · 8
Projective space → At, Euclidean, Historically, In, It, Synonyms, The, These
related to External links · 6
Projective space → Eric, MathWorld, PlanetMath, Projective Planes, Small Order, Weisstein

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Important terminology

projective space points lines two one geometry spaces set line point dimension vector plane field defined called coordinates infinity intersection

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Projective spaceis atopological space0.90text
Projective spaceis amanifold0.90text
Projective spaceis asubset X0.90text
Projective spaceis aprojective space where P is a finite set of points0.90text
elliptic curves of a given kind. other ringsGeneralizing to associative ringsinstance ofmoduli spaces parametrize objects0.80text
Projective spacerelated to Algebraic geometryOriginally0.60section
Projective spacerelated to Algebraic geometryThese0.60section
Projective spacerelated to Algebraic geometryIt0.60section
Projective spacerelated to Algebraic geometryFor0.60section
Projective spacerelated to Algebraic geometryIn0.60section
Projective spacerelated to Algebraic geometryBézout's0.60section
Projective spacerelated to Algebraic geometryAnother0.60section

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