Abstract: If we know they Hausdorff dimension of two metric spaces, do we know any other connection between the spaces? A good place to start would be to understand the connection between compact metric spaces and products of the unit interval. We will prove that a compact metric space of Hausdorff dimension strictly greater than k can be mapped onto the k-dimensional cube by a Lipschitz function. This result was proved by Keleti, Mathe, and Zindulka in 2012, but is an answer to an issue raised by Kolmogorov in 1932. There are known counter examples if the compact metric has Hausdorff dimension k