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Let us consider the vector space T_p. Its projectivization PTₚ, is a projective space, which is obtained from T_p, by factorization relative to the collinearity of vectors. The projectivization PTₚ is a set of straight lines, passing through the point p. Under projectivization, the cone C(2,r) becomes a manifold S(1,r-1) of dimension r.

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