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projective plane

under non-zero scalar multiplication. Elements are sets of

the form

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".