No abstract

We propound some convergence theory for quasimetric spaces that includes as a particular case the Gromov-Hausdorff theory for metric spaces. We prove the existence of the tangent cone (with respect to the introduced convergence) to a quasimetric space with dilations and, as a corollary, to a regular quasimetric Carnot-Carathéodory space. This result gives, in particular, Mitchell's cone theorem.

We establish upper bounds on bit complexity of computing solution operators for symmetric hyperbolic systems of PDEs, combining symbolic and approximate algorithms to obtain the solutions with guaranteed prescribed precision. Restricting to algebraic real inputs allows us to use the classical (“discrete”) bit complexity concept.