Spatial unity for the apperception engine

We develop a logical approach for computational agents to spatially explore their environment, extending on the Kant-inspired logical unification methods of the Apperception Engine. Evaluating models of the Regional Connection Calculus as Alexandroff Topologies, we axiomatise connectedness and unity of space. We further define dimensionality for tolerance spaces and prove that locally verifiable properties guarantee global consistency of space as the existence of isomorphisms to grids, turbands or tori. Finally, we provide a generally competent and explainable computational agent that unifies intuition in space, the Spatial Apperception Engine.