تقرير
Finite asymptotic clusters of metric spaces
| العنوان: | Finite asymptotic clusters of metric spaces |
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| المؤلفون: | Bilet, Viktoriia, Dovgoshey, Oleksiy |
| سنة النشر: | 2018 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Metric Geometry, 54E35, 05C12, 05C69 |
| الوصف: | Let $(X, d)$ be an unbounded metric space and let $\tilde r=(r_n)_{n\in\mathbb N}$ be a sequence of positive real numbers tending to infinity. A pretangent space $\Omega_{\infty, \tilde r}^{X}$ to $(X, d)$ at infinity is a limit of the rescaling sequence $\left(X, \frac{1}{r_n}d\right).$ The set of all pretangent spaces $\Omega_{\infty, \tilde r}^{X}$ is called an asymptotic cluster of pretangent spaces. Such a cluster can be considered as a weighted graph $(G_{X, \tilde r}, \rho_{X})$ whose maximal cliques coincide with $\Omega_{\infty, \tilde r}^{X}$ and the weight $\rho_{X}$ is defined by metrics on $\Omega_{\infty, \tilde r}^{X}$. We describe the structure of metric spaces having finite asymptotic clusters of pretangent spaces and characterize the finite weighted graphs which are isomorphic to these clusters. Comment: 38 pages, 3 figures. arXiv admin note: text overlap with arXiv:1708.05235 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1801.01014 |
| رقم الأكسشن: | edsarx.1801.01014 |
| قاعدة البيانات: | arXiv |
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