This article is cited in 14 papers

The tangent cone to a quasimetric space with dilations

S. V. Selivanova

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

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.

Keywords: quasimetric space, Gromov–Hausdorff convergence, metric tangent cone, Carnot–Carathéodory space, dilation.

UDC: 515.124+514.753.28

Received: 21.11.2008
Revised: 03.06.2009

 English version: Siberian Mathematical Journal, 2010, 51:2, 313–324

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