A projective space is defined as a quotient of a vector space under the equivalence relation x ~ y <=> (exists k =/= 0 such that x = ky). https://en.wikipedia.

A projective space is defined as a quotient of a vector space under the equivalence relation x ~ y <=> (exists k =/= 0 such that x = ky). https://en.wikipedia.org/wiki/Projective_space#Definition https://en.wikipedia.org/wiki/Projective_space#Definition