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-   -   Real Projective Plane, Intersections, Bijections (https://www.askmehelpdesk.com/showthread.php?t=448608)

  • Feb 18, 2010, 09:00 AM
    mavroulis
    Real Projective Plane, Intersections, Bijections
    Um, I have these exercises for practising but I am really struggling doing them. I just need someone to help me with that so as to have some solutions in order to practise with and revise. Thank you in advance for your help.


    Let Λ be a line in Real Projective Plane and its equation:
    Ax + Bu + Ct = 0.
    Let Λx, Λu, Λt be the lines in Real Projective Plane given by x = 0, u = 0, t = 0, respectively.

    1)Find the intersections of Λx with Λu,Λx with Λt and Λt with Λu,

    2)Find the intersection of Λ1 with Λ2 which is a subset of the Real Projective Plane, where Λ1 and Λ2 are lines in that, given by the equations x+u+t=0 and x-u=0 respectively.

    3)Construct bijections Λx-> RP1 and Λu-> RP1 and Lt-> RP1 (Real Projective.. )

    4) Put Ax = RP2 \ Λx, put Au = RP2 \ Λu, put At = RP2 \ Λt.
    Show that :RP2 = Ax U Au U At (U is for union)

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