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Math Help - Antenna of the Mandelbrot Set.

  1. #1
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    Antenna of the Mandelbrot Set.

    Hello, I am having troubling proving the antennas of the Mandelbrot Set have empty interior.

    I have seen it done for a none general point on an antenna (not rigorously), for instance let c=-0.75+0i then it is easy to show any point of the form c=-0.75+ni for n>o escapes to \infty but I don't know how to start proving this for a general point, and without using the above method, which obviously doesn't suffice as a proof.

    I realise this point isn't on an antennae, I was just giving an example of how I would "show" a point has 0-thickness.
    Last edited by skamoni; October 29th 2010 at 07:37 AM.
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