BANACH-TARSKI THEOREM AND CANTORIAN MICRO SPACE-TIME

Starting from the cosmic initial singularity scenario and general relativity, Banach-Tarski theorem together with the theorem of Mauldin-Williams leads to the conclusion that micro space should resemble a realization of a random quasi-transfinite four-dimensional Cantorian manifold (d(c)((4))))with a Golden Mean Hausdorff dimension at the core (d(c)((0)))) where d(c)((0)) = \[d(c)((0))\d(c)((0))]\ and [d(c)((0))\ = 0 - id(c)((0))). In the imaginary phase space the dimensionality (the number of components) is eight and is related to SU(3) and quarks.