 In “On the Hypotheses Underlying Geometry,” Riemann focuses on how to determine the overall topological properties of space. Topological properties are those spatial properties of figures that are invariant under transformation, that is, that stay the same when the figures move. Riemann proves that a space of n dimensions, that is, a space determined by n continuously and independently varying magnitudes, has constant curvature, but only under the hypothesis that all spatial figures can be moved or rotated anywhere in space without changing their form, the so-called “Axiom of Free Mobility” (cf. Königsberger 1906, 260–261). For the case of astronomy, Riemann observes: 