  We introduce a pregeometry that provides a metric and dimensionality over a
Borel set (Wheeler's "bucket of dust") without assuming probability amplitudes
for adjacency. Rather, a non-trivial metric is produced over a Borel set X per
a uniformity base generated via the discrete topological group structures over
X. We show that entourage multiplication in this uniformity base mirrors the
underlying group structure. One may exploit this fact to create an entourage
sequence of maximal length whence a fine metric structure. Unlike the
statistical approaches of graph theory, this method can suggest dimensionality
over low-order sets. An example over Z2 x Z4 produces 3-dimensional polyhedra
embedded in E4.

General Relativity and Quantum Cosmology