Local approximation of uniformly regular Carnot–Carathéodory quasispaces by their tangent

We prove a local approximation theorem for the Carnot–Carathéodory quasimetrics on uniformly regular (equiregular) Carnot–Carathéodory spaces. Using this theorem, we study convergence of the Carnot–Carathéodory quasispaces to their tangent cones. In particular, we prove a Mitchell type theorem on convergence of an equiregular Carnot–Carathéodory quasispace with distinguished point to its tangent cone.