  While the Vietoris-Rips complex is now widely used in both topological data
analysis and the theory of hyperbolic groups, many of the fundamental
properties of its homology have remained elusive. In this article, we define
the Vietoris-Rips homology for semi-uniform spaces, which generalizes the
classical theory for graphs and metric spaces, and provides a natural, general
setting for the construction. We then prove a version of the Eilenberg-Steenrod
axioms in this setting, giving a natural definition of homotopy for
semi-uniform spaces in the process.
