The existence of a tangent cone to a quasimetric Carnot-Caratéodory space at a regular point is studied. The structure of the space is specified by smooth vector fields and its local Lie group is a Carnot group. The distance between quasimetric spaces is defined as the infimum and is finite for bounded quasimetric spaces. A sequence of compact quasimetric spaces is found to converge to a compact quasimetric space and the compact quasimetric spaces are the limits of the same sequence of compact spaces. The Gromov-Hausdorff distance between metric spaces is defined as the infimum for which there exists a metric space its subspaces isometric to the spaces. The results show that the convergence of vector fields is uniform in g from some compact neighborhood and that the quasimetric space is the tangent cone to the quasimetric space.
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