projective plane

[prə′jek·tiv ′plān] (mathematics) The topological space obtained from the two-dimensional sphere by identifying antipodal points; the space of all lines through the origin in Euclidean space. More generally, a plane (in the sense of projective geometry) such that (1) every two points lie on exactly one line, (2) every two lines pass through exactly one point, and (3) there exists a four-point.

Projective Plane

in its original meaning, the Euclidean plane with the addition of the points and line at infinity. From the topological standpoint, the projective plane is a closed, non-orientable surface with Euler characteristic 1.

projective plane

(mathematics)The space of equivalence classes of vectorsunder non-zero scalar multiplication. Elements are sets ofthe form

kv: k != 0, k scalar, v != O, v a vector

where O is the origin. v is a representative member of thisequivalence class.

The projective plane of a vector space is the collection ofits 1-dimensional subspaces. The properties of the vectorspace induce a topology and notions of smoothness on theprojective plane.

A projective plane is in no meaningful sense a plane and wouldtherefore be (but isn't) better described as a "projectivespace".

单词	projective plane
释义	projective plane projective plane [prə′jek·tiv ′plān] (mathematics) The topological space obtained from the two-dimensional sphere by identifying antipodal points; the space of all lines through the origin in Euclidean space. More generally, a plane (in the sense of projective geometry) such that (1) every two points lie on exactly one line, (2) every two lines pass through exactly one point, and (3) there exists a four-point. Projective Plane in its original meaning, the Euclidean plane with the addition of the points and line at infinity. From the topological standpoint, the projective plane is a closed, non-orientable surface with Euler characteristic 1. projective plane (mathematics)The space of equivalence classes of vectorsunder non-zero scalar multiplication. Elements are sets ofthe form kv: k != 0, k scalar, v != O, v a vector where O is the origin. v is a representative member of thisequivalence class. The projective plane of a vector space is the collection ofits 1-dimensional subspaces. The properties of the vectorspace induce a topology and notions of smoothness on theprojective plane. A projective plane is in no meaningful sense a plane and wouldtherefore be (but isn't) better described as a "projectivespace".
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