Relation between Pn(homo)and Rn(in- homo) Rn--> Pn, extension, embedded in Pn--> Rn, restriction. P2 and r2 R2>P2 xy H y finite pts x3=1≠0 P2→>R2:|x,| x3 for finite pts x≠0, and line at inf x,=0
16 P2 and R2 and line at inf. 0 : for finite pts 0, 3 3 3 1 3 1 3 2 1 = → x x x x x x x x x P 2 R 2 finite pts 1 0 1 : 3 = → y x x y x R 2 P 2 Relation between Pn (homo) and Rn (in-homo): Rn --> Pn, extension, embedded in Pn --> Rn, restriction
One example of construction of projective line by quotient space
17 One example of construction of projective line by quotient space
Examples of projective spaces Projective plane p2 Projective line p1 Projective space P3
18 Examples of projective spaces • Projective plane P2 • Projective line P1 • Projective space P3