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Projective plane

<mathematics> 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".

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