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Sibirskii Matematicheskii Zhurnal, 2010, Volume 51, Number 2, Pages 388–403
(Mi smj2092)
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This article is cited in 14 scientific papers (total 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.
Received: 21.11.2008 Revised: 03.06.2009
Citation:
S. V. Selivanova, “The tangent cone to a quasimetric space with dilations”, Sibirsk. Mat. Zh., 51:2 (2010), 388–403; Siberian Math. J., 51:2 (2010), 313–324
Linking options:
https://www.mathnet.ru/eng/smj2092 https://www.mathnet.ru/eng/smj/v51/i2/p388
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Abstract page: | 439 | Full-text PDF : | 151 | References: | 52 | First page: | 5 |
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