IRRATIONAL POINTS IN THE MANDELBROT SET.

The continuity of the map φ : c → dimH(Jc) where Jc is the Julia set of the map fc(z) = z2 + c is discussed in this paper. Using the Hausdorff dimension, a partial order is defined on the Mandelbrot set M. Some properties of irrational points defined by this order are also studied. [ABSTRACT FROM AUTHOR]