| slovo | definícia |
projective plane
(foldoc) | projective plane
The space of equivalence classes of vectors
under non-zero scalar multiplication. Elements are sets of
the form
kv: k != 0, k scalar, v != O, v a vector
where O is the origin. v is a representative member of this
equivalence class.
The projective plane of a vector space is the collection of
its 1-dimensional subspaces. The properties of the vector
space induce a topology and notions of smoothness on the
projective plane.
A projective plane is in no meaningful sense a plane and would
therefore be (but isn't) better described as a "projective
space".
(1996-09-28)
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