Abstract
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.
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