We explore the possibility that black holes and Space could be the geometrically Compactified Transverse Slices ("CTS"s) of their higher (+1) dimensional space. Our hypothesis is that we might live somewhere in between partially compressed regions of space, namely 4d_{L+R} hyperspace compactified to its 3d transverse slice, and fully compressed dark regions, i.e. black holes, still containing all _{L}d432-1-234d_{R} dimensional fields. This places the DGP, ADD, Kaluza-Klein, Randall-Sundrum, Holographic and Vanishing Dimensions theories in a different perspective.

We first postulate that a black hole could be the result of the compactification (fibration) of a 3d burned up S^{2} star to its 2d transverse slice; the 2d dimensional discus itself further spiralling down into a bundle of one-dimensional fibres.

Similarly, Space could be the compactified transverse slice (fibration) of its higher 4d_{L+R} S^{3} hyper-sphere to its 3d transverse slice, the latter adopting the topology of a closed and flat left+right handed trefoil knot. By further extending these two ideas, we might consider that the Universe in its initial state was a "Matroska" 4d_{L+R} hyperspace compactified, in cascading order, to a bundle of one-dimensional fibres. The Big Bang could be an explosion from within that broke the cascadingly compressed Universe open.