On the Gromov-Hausdorff limit of metric spaces

Rok, strany: 2019, 931 - 938

In this paper, we show that a class of metric spaces determined by a continuous function $f$, which defines on the metric space of all real, $n× n$-matrices $m$ is closed under the Gromov-Hausdorff convergence. This conclusion can be used to prove some metric properties of metric space is stable under the Gromov-Hausdorff convergence. Secondly, we consider the stability problem in Gromov hyperbolic space and show that if a sequence of Gromov hyperbolic spaces $(X_n,d_n)$ is said to converge to $(X,d)$ in the sense of Gromov-Hausdorff convergence, then the Gromov hyperbolicity $δ(X_n)$ of $(X_n,d_n)$ tends to the Gromov hyperbolicity $δ(X)$ of $(X,d)$.

ISO 690:

Wu, Z., Xiao, Y. 2019. On the Gromov-Hausdorff limit of metric spaces. In Mathematica Slovaca, vol. 69, no.4, pp. 931-938. 0139-9918. DOI: https://doi.org/ 1515/ms-2017-0278

APA:

Wu, Z., Xiao, Y. (2019). On the Gromov-Hausdorff limit of metric spaces. Mathematica Slovaca, 69(4), 931-938. 0139-9918. DOI: https://doi.org/ 1515/ms-2017-0278

Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava